In order to determine that some piece of culture has been inherited over the generations, it's best to study a piece that is not strongly shaped by material concerns -- and food certainly is. Not just the local environment containing different raw materials, but convergent evolution that could make two disparate lineages appear to share a common source.
For example, all pastoralist cultures will include dairy products in some way, even though some of them evolved separately and independently of each other way back when. At this level, you can't tell which ones share a common ancestor. But perhaps there are finer-grained aspects of their dairy culture that do in fact distinguish one from the other. That is true for Indo-Europeans as contrasted with Hamito-Semites, but that's a broad topic for another post.
To ease back into the subject matter, we'll start with a more specific case -- desserts for the New Year's celebration. As far as I can tell, this is an original discovery.
One crucial criterion I set for the earlier analysis was looking at pieces of culture that are highly ritualistic, as these are less susceptible to alteration -- which amounts to sacrilege -- and less influenced by foreign customs. That impedes the two major sources of change (from within and from without).
For mundane culture, you might adopt some other group's street food if it tastes good, but you're not going to adopt their culinary rituals for some holiday that you don't even celebrate yourself, and which might displace your own rituals for the holidays that you do actually celebrate.
And ritualistic pieces of culture are not so strongly influenced by material, utilitarian concerns. Making do with what you've got in order to not starve on a daily basis, could easily shape two distinct food cultures into similar ones, if their environmental pressures were similar. But what you eat, and how you prepare it, for some rare holiday -- that's not going to make or break your health on a quotidian level. You can keep doing it in the inscrutable, not-so-instrumental way without plunging your family into starvation.
That is the approach of genetics in reconstructing who came from where, and who is related to who else by what degree. You look at parts of the genome that are neutral in an adaptive sense. It's like an ID number generated at random, and whose digits do not influence anything about your ability to survive and reproduce. So if you and someone else have the same ID number, you must be closely related. Imagine flipping a million-sided die and getting the same number twice -- that's no coincidence, and both of your numbers must have descended from a single die roll in the past belonging to a shared ancestor.
For the current case, the epiphany came after looking into Armenian food culture. They are Indo-Europeans who have been holed up in the Caucasus highlands and mountains for millennia, and mountains are harder for foreigners to invade. If you can't invade physically, you can't invade culturally. All three branches of the Indo-European language family that have only one surviving member are located in hilly / mountainous terrain -- Albanian, Greek, and Armenian, who have resisted the spread of far more numerous sister branches (Slavic for the first two, Indo-Iranian for the last one).
A staple of Armenian food culture is a large sweet bread called gata. On a special occasion, they put something special in the dough -- a button or a coin (or perhaps some other trinket in some other local variation). Whoever gets the piece with the hidden prize is supposed to have good luck for the rest of the year. This special occasion is Candlemas, which marks the end of the Christmas / Epiphany season, and in that way is timed with the end of the old year and beginning of the new year.
This is a clear counterpart to various traditions throughout Europe, all of which are timed around the New Year, although perhaps Christianized in some way (Christmas, Mardi Gras, etc.). There's the king's cake from Spain and France, the vasilopita in Greece and similar non-Christianized versions in the Balkans and Eastern Europe, the Christmas pudding in Britain, and the Christmas rice pudding in Scandinavia.
In fact, there's an even older pre-Christian version from the Roman holiday of Saturnalia, also timed around the end of December. As part of the carnivalesque inversion of the social hierarchy, a King of Saturnalia was chosen from the lower-ranking members, to preside over the merrymaking. He was chosen by lot -- a cake was baked with a bean somewhere inside the dough, and whoever got the piece with the bean had the good fortune of assuming the role. (This good luck is shorter in duration, although higher in intensity and more palpable, compared to the later interpretation that it was generic yearlong good luck.)
We could say that it all began with the Romans and was inherited by former political colonies of the Roman Empire, or by cultures that owed their Christianity to Roman influence. But perhaps the current variety of traditions do not stem from a Roman source, but are descendants of an even older ancestor, such as Indo-European. In that view, the British custom came from a Celtic source, the Scandinavian custom from a Germanic source, the Ukrainian custom from a Slavic source, etc. Only the Western Mediterranean customs would come from an Italic source, in this view.
This is how we analyze the languages spoken by these groups. If the word for "three" appears so similar across all of them, it's not necessarily because they all descend from Latin via the Roman Empire's influence and colonization. It's because each of them has its own older source, which is only Latin for the Romance branch, but those older sources themselves have an even older source in common -- Proto-Indo-European.
Still, if we only restrict our investigation to Europe, it can be hard to conclude decisively one way or another, because there are so few cases that can only be interpreted to support one view rather than the other view. That's why we have to look at the broader Indo-European spectrum.
And the example from Armenia argues strongly in favor of the Indo-European roots of the tradition, since most of Greater Armenia was not politically conquered by the Roman Empire, nor was its primary cultural influence from Rome. In antiquity, it was torn between the Romans and the Persians (who did not practice Saturnalia, and who would never become Christian). If Armenia did not receive these traditions through contact with the Romans, then they must have already been in place due to shared ancestry with an even older Indo-European origin.
The Roman Empire / Christian origin can also be ruled out from the other direction, by looking at cultures that were part of the Roman Empire, some of whom also became Christian, but who are Hamito-Semitic rather than Indo-European. That includes North Africa and the Levant. The obvious test is Lebanon (both a former Roman colony and early Christians). Although their Christmas dessert is a rice pudding, it does not involve the tradition of hiding an item that will bring good luck to whoever receives that portion.
That reflects the wider similarities in food culture between the Levant and non-Indo-European cultures of the region, but we'll get back to that topic when we explore the use of dairy among Indo-European vs. Hamito-Semitic cultures.
But by far the clearest evidence of the Indo-European origin of this tradition is the rituals involved in making and eating samanu in the eastern, Indo-Iranian range of the I-E territory. The special occasion is Nowruz, the New Year, celebrated in Iran, Afghanistan, and other areas nearby. Like Saturnalia being pre-Christian, Nowruz is pre-Islamic. Samanu is a sweet pudding made from wheatgrass, cooked in large pots.
In Afghanistan and Uzbekistan the whole gathering, mostly women, gather near the huge pot: sit in a circle, sing songs, have fun, each of them waits for their turn to stir the sumalak [AKA samanu]. While stirring the samanak [AKA samanu], wishes can be made. Also, whole walnuts are thrown in near the end of the preparation while making a wish.
In her book Recipes from My Persian Kitchen, Nasreen Zereshki mentions that finding an unshelled nut in your serving of samanu is a "good omen". These are intended to be inedible trinkets or charms, since they are left unshelled, as opposed to shelling nuts when used as raw ingredients for an edible meal.
This exactly parallels the Christmas pudding rituals from the opposite side of the I-E territory, among the Celts (British). From Wikipedia's article on Stir-up Sunday:
Everyone takes a turn to stir the pudding mix for each person involved is able to make a special wish for the year ahead. Practically, stirring the mixture is hard work, therefore as many as possible are involved... In some households, silver coins are added to the pudding mix. It is believed that finding a coin brings good luck.
The special occasion is the New Year, a sweet pudding is being made in a pot, a group has gathered socially (not just one cook), they take turns stirring, each one makes a wish as they do so, some charms are thrown into the mix, and whoever gets one in their serving will enjoy good luck.
I tried looking for a counterpart in the Indian subcontinent, but could not easily find one -- it's too diverse, and with several potential holidays to sift through. I'm sure there's something there, just not an example I could identify right away. My targets are Pakistani and NW Indian customs for Diwali, Holi, and Lohri, although hopefully their Muslims are similar to European Christians in preserving local pagan traditions for nominally Abrahamic occasions.
I'd also like to find a counterpart in Turkey, which is more Indo-European than Hamito-Semitic (and is Turkic in language only, from known invaders). Ideally from their pre-Islamic celebrations, akin to Nowruz further to the east.
Still, this is mind-blowing stuff for archaeologists of culture. Why hasn't the connection been made before? Because academics are cerebrals and blind to most of material culture. They will notice that languages and mythologies are shared at a deep level among Indo-Europeans, but not their corporeal folkways. Sure, they know about the shared subsistence modes and basic ecosystems, like the I-E people having words for snow and cows. But not what we would call folk culture, customs, rituals, and the like -- especially by investigating those folkways directly, rather than through linguistic hints.
Those rituals are still being performed to this day, for similar purposes as before. So why not investigate their lineages? Not because they're fuzzy rather than sharply defined -- again, academics have no problem positing a shared pantheon, mythological narratives, and other things that are less clearly defined than "the pronunciation of the word for 'cow'". It's because they're too much a part of corporeal activities.
That's why I'm focusing on the topics I've chosen -- iconography, dance, wedding customs, and now food. It's mostly untapped, but no less important to appreciating the deep roots of all these seemingly disparate cultures today.