For the carnival doughnuts, heat about 100 ml of the milk and dissolve the yeast in it, mix with 80 g of the flour to form a dampfl. Sprinkle the dampfl with flour, cover and let it rise in a warm place for about 30 minutes. Beat eggs, salt, sugar and vanilla sugar until foamy.
Stir in remaining milk and rum. Knead the mixture with the remaining flour, steam and butter to form a smooth dough. Flour the dough, cover with a kitchen towel and let it rest at room temperature for about 1 hour – it should double in volume.
Knead the dough briefly and form into a roll on a floured work surface. Cut off 20 pieces weighing approx. 50 g from it and grind into balls on an unfloured work surface.
Place a cloth on an upturned baking sheet, sprinkle with flour. Place dough pieces on top, cover with cloth. Place a second baking sheet on top.
Flatten doughnuts slightly, they should be the same height. Lift off tray, cover doughnuts with cloth and let rise at room temperature for about 30 minutes. Heat oil to 170 °C about 4 fingers high.
Place doughnuts upside down in oil, cover and bake for approx. 1 minute, turn and bake uncovered for approx. 1 minute until done.
Lift out and drain on paper towels. Fill the jam into a piping bag with a doughnut nozzle and squirt into the doughnuts. Sprinkle the doughnuts with powdered sugar.