Place 3 eggs and 1 cup of sugar into the bowl of a stand mixer; beat on high speed until thick and pale (about 3 min).
Heat 1 cup of milk and 3 tbsp of butter in the microwave to boiling point (up to 3 minutes, keep your eye on it as milk can run over).
Add 1 cup of flour to the beaten eggs and mix over medium speed. With the mixer still running slowly pour in the steaming hot milk and mix for about a minute. Cover and allow to sit for 15 min.
Heat remaining 1 cup of milk in a microwave for about 1 minute. Milk should be warm, NOT hot; if you stick your finger in the milk, it should feel a little warmer than lukewarm. Not by any means hot. Add 1 tbsp of dry yeast and 1 tbsp of sugar; stir and allow to sit for 15 min.
After 15 minutes add the yeast mixture to the egg mixture. Then add ¼ tsp baking powder, 1 tsp vanilla sugar, 1 ½ tsp salt, 1 cup sour cream, and 2 ½ cups flour; whisk well. Cover and allow to sit for 45 minutes.
After 45 minutes add 3 cups of flour and ⅓ cup of oil. Knead over low-speed for 10 minutes, adding remaining ¼ cup of flour towards the end. Cover bowl and allow to rise for 2 hours or until the dough has doubled in size.
Once the dough has risen and doubled in size; remove onto a well-floured surface. Form dough into a 20" log and cut into five equal pieces.
Working with one piece at a time, shape into a ball by flipping over and pinching down all sides. Roll out into a 12" circle and using a pizza cutter slice dough into eight equal pieces.
Place one heaping tsp of filling into the broadest part of the triangle. Seal filling by pinching down the sides and top. Once the mixture is sealed lightly fold over the flap and pinch the very end to the bottom of the bun.
Line two 13" by 9" pans with parchment paper and transfer rolled buns into the pan. You should have about three rows down on each pan. Allow prepared bulochki to rise in a warm place for 1 hour, covered.
Preheat the oven to 350 degrees F. Brush with beaten egg wash over the top. Bake for 35-40 minutes, rotating if necessary.
Dissolve 2 tbsp of sugar in ¼ cup of water in a small bowl and brush over hot buns.
