In a small bowl, combine the yeast, 1 tablespoon flour, 1 tablespoon sugar, and water. Mix well, cover, and allow to rest until the mixture becomes foamy.
In another large bowl, mix the remaining 3 cups of flour with the schmaltz, salt, remaining sugar, and the egg yolks.
After the batter has risen, punch it down and transfer it to a lightly floured surface. Roll out the dough to a 3/4-inch thickness. Use a round cookie cutter or a glass with a 2 1/2- to 3-inch opening to cut circles out of the dough.
Place a teaspoon of shredded meat in the center of each circle, and then cover with another circle of dough. Make sure that 2 circles attach well to form a closed ball with the meat in the middle. You’ll use less meat than you think — but don’t overdo it or they will open up.
Cover the doughnuts with a clean, slightly damp tea towel and allow to rise until puffed up, about 45 minutes to 1 hour.
Line a large plate or platter with several layers of paper towels and set aside.
Pour 2 inches of oil into a deep, heavy-bottomed pot. Heat over medium-high heat until a deep-
registers 350 F (180 C).
Working in batches, carefully slip the doughnuts into the oil, taking care not to crowd the pan. Fry the doughnuts on both sides until puffed and golden brown, about 2 to 3 minutes per side. Carefully remove the doughnuts with a slotted spoon and transfer to the towel-lined plates to drain.
Cool slightly, and serve immediately.