According to John Cooper's book Eat and be Satisfied, the tradition of dairy foods for Shavouth began in Europe in the Middle Ages. He quotes a thirteenth-century philosopher who said that the appropriate food for the festival was milk and honey, to commemorate the giving of the Torah on Mount Sinai, subject of the celebration. In Provence in the fourteenth century, a special honey cake was baked in the shape of a ladder.
In the later Middle Ages, an abundance of milk in this season led to dairy products being chosen for the festival. Also, dairy dishes were the food for the Christian festival of Whitsun, or Pentecost, occurring at the same time as Shavouth -- and Jews may have been influenced by their neighbors. In the fifteenth century, Jews baked a big floden cake made with milk and raisins, called Sinai Cake.
Blintzes -- pancakes filled with farmer's cheese -- were related to similar dishes in Ukrainian and Russian cooking called blini, according to Cooper. Claudia Roden says they are of Hungarian origin. In the shtetls of Eastern Europe, milk was also abundant in late May or early June. The traditional Shavouth dairy meal included a saffron-glazed challah, as well as blintzes, beet borscht with sour cream, babkas, and other dairy dishes.
The Jews of Arab countries had a wide variety of celebrations of the festival. In Persia and North Africa, it was associated with roses or other flowers, and worshipers were sprinkled with rose water. Dairy products are used throughout the Jewish world: "in Kurdistan a meal is made of wheat ground in sour milk and rissoles filled with cheese and butter instead of meat. In Afghanistan the Jews cook rice in butter, pouring a specially prepared thin yoghurt over it. In the Ladino-speaking communities of the Middle East large seven-tiered challah filled with sweetmeats is baked." (Lilian Cornfeld, Israeli Cookery, p. 262-264)
Cheesecake was the tradition in some European Jewish communities. I read: "Italian Easter cheesecake, which is made with citrus rind and fragrant orange blossom water ... is now served in Italy for Shavuot. Israelis eat a light and creamy mousselike cheesecake made with gvina livana, or white cheese. Cheesecakes in France are most often made with fresh farmer’s cheese or savory goat cheese, while Greek cheesecake recipes call for feta or for Greek yogurt." (The Great Cake Debate: A Taste of History Behind a Shavuot Tradition)
Another explanation of the dairy tradition -- an article titled Cheese blintzes wrapped in tradition for Shavuot -- is more folkloric:
While no one knows for sure what the ancient Israelites ate after receiving the Torah, historians speculate that they didn’t keep kosher until encountering the dietary laws found in this sacred scroll. Because they couldn’t immediately change their ways, their only option was to eat a dairy meal until they could make kosher their cooking utensils and meat.TABLET online magazine had a complete description of the holiday, including this about dairy food:
WHAT DO WE EAT?Joan Nathan wrote in another Tablet article that all dairy-making cultures use milk products in their spring festivals. She also associates cheese with Mount Sinai, where Moses received the 10 commandments on the first Shevouth:
Delicious dairy products. Cheesecakes are big. If your ancestors hail from the Tri-State area—Poland, Russia, Ukraine—so are blintzes.
The rational explanation is that the Torah was given on the Sabbath, and as no animals could be slaughtered to celebrate the happy occasion, the Israelites likely shrugged their shoulders and collectively agreed to nosh on some brie. More mystical Jews—you know, Madonna—believe that the numbers speak for themselves: Dairy in Hebrew is chalav, and if you sum up the numerical value of the three Hebrew letters that make up that word you get 40. Which is a number you’d remember if you had to wander in the desert for as many years.
As for Mount Sinai, it’s known by other names: Mountain of God, mountain of Bashan, and mountain of peaks (Har Gavnunim) all mentioned in the 68th psalm. Gavnunim means “gibbous, many-peaked,” but the word has the same root as g’vinah, meaning cheese. Accordingly, cheese consumption at this time of year is a reminder of the giving of the Law. And, throughout the Bible, Israel is repeatedly referred to as the land of milk and honey.So there are lots of explanations of those blintzes. Too many.