For the hamburger buns, stir yeast with sugar until liquid. Heat butter and 250 ml milk. Add 125 ml water and let it cool down lukewarm. Put 1 tsp. salt, flour and egg in a bowl. Add the milk mixture.
Add the yeast mixture and immediately knead into an elastic dough with the dough hooks of the hand mixer for 6-8 minutes. Cover and leave to rise in a warm place for about 45 minutes.
Onions peel, in fine rings cut or plane. Put them in a pot with brown sugar and heat them up for about 5 minutes. Deglaze with port wine and season with salt and pepper. Let it simmer open for about 35-40 minutes.
Knead the dough briefly on a floured work surface. Form about 30 round dough pieces from the dough and place them on two baking trays lined with baking paper. Cover them and let them rise for another 20 minutes.
Whisk the egg yolks with 2 tablespoons of milk. Spread the bread roll with it and sprinkle with sesame seeds. Bake in the preheated oven (electric cooker: 200 °C/ convection oven: 175 °C/ gas: see manufacturer) one after the other for about 15 minutes.
Remove and let it cool down on a cake rack.
Season onion jam with vinegar. Let it cool down. Season minced meat with 2 tsp salt and pepper. Form about 30 small meatballs from the mixture. Heat the oil in a large frying pan, fry the meatballs for 4-5 minutes while turning.
Drain on kitchen paper. Sort the salad, wash, clean and pat dry. Cut cheese slices into 4 squares. Cut burger buns in half crosswise. Cover halves with onion jam, meatballs, salad and cheese.
Put the lid on. If necessary, fix it with wooden skewers.