Sieve or mix the cottage cheese until smooth. If it is too wet, let it drain. In a bowl, mix the cottage cheese with egg yolks, sugar, vanilla extract, and salt.
Sift the flour with baking powder and gradually mix into the cottage cheese mixture. A soft, slightly sticky dough will form. Do not knead it for too long, or it will be tough.
Divide the dough into 8 equal parts for the donuts and 4 smaller parts for the 'hats'.
Shape the larger part into a disc and make a hole in the center (with your finger or a small cutter). Make a small ball (hat) from the smaller part.
Heat the oil in a pot to medium temperature (about 170 °C (338 °F)).
Place 2-3 donuts and 1-2 balls at a time and fry for 3-4 minutes on each side until golden brown. Remove and place on a paper towel to remove excess oil.
Place a hot Papanași (donut) on a plate. Add a large spoonful of sour cream in the center and around it.
Drizzle generously with jam and place the small fried ball on top of the 'donut'. Dust with powdered sugar and serve immediately.