In the bowl of a stand mixer, combine yeast with two cups of warm milk (110°F) and one tablespoon of sugar. Let this mixture rest on the counter for 10 minutes.
Add the eggs, mayonnaise, salt, and remaining sugar to the mixture, whisking to combine.
Gradually mix in the flour with a spatula. Once the flour is all mixed in, add oil to the mixture. It's important to add the oil last, as this helps with the dough texture. Use a stand mixer fitted with a dough hook to knead the dough until it's elastic, this will take at least 10 minutes. The dough should not be sticky, but still soft. Then, allow the dough to rise for about an hour.
Cut the dough into 30 equal pieces (a dough or bench scraper works great here). Shape each piece into a flattened ball. Place the balls 2 inches apart on a parchment lined baking sheet, and cover with a towel. Let them rise for 30 minutes.
After rising, press each bun in the center with the bottom of a glass to hollow out the center for the filling. You'll want to space out the balls of dough before pressing into them, so that the pastries don't touch. Use two baking sheets to fit all of the buns.
Whisk the cream cheese, cottage cheese, eggs, and sugar together to create the filling. Optionally, you can add raisins to the filling. (Note: If adding raisins, they will need to be soaked in boiled water for 10-15 minutes and then drained, before combining with the cheese.)
Fill each center with the sweet cheese filling.
Preheat oven to 350°F. Bake one tray of vatrushka buns at a time, the other tray can rest on the counter in the meantime. Bake for 30 minutes or until golden brown. Enjoy!