Bake the potatoes in their skins (in a preheated oven at 200°C, for about 45-50 minutes), scoop out the flesh, and while still warm, pass through a sieve.
Put the sieved potato in a bowl, add the egg yolks, the yeast dissolved in the lukewarm milk, the melted butter and a pinch of salt.
Mix well, then add enough flour to make a dough that's much firmer than a strudel dough, but still easy to knead.
Work it well with a spoon, then cover with a kitchen towel and let rise in a warm place for about 30-40 minutes, until visibly doubled.
Meanwhile make the filling: mix the ground ham with the egg yolk, the sour cream, salt and a little ground pepper.
Flatten the risen dough on a floured surface to a finger's thickness, and cut out rounds with a cookie cutter or a glass.
Put a hazelnut-sized amount of ham filling in the center of each round, place a smaller round of dough on top, and press the edges together.
Place the doughnuts on a floured board, and let rise again for 15-20 minutes.
Fry in plenty of hot oil (about 170°C), until golden brown on both sides.
Roll in grated parmesan while still warm, and serve immediately.
Based on: Malatinszky Fanny szakácskönyve (a classic Hungarian cookbook), modernised. Calories and protein are estimated.