Melt the butter, either in a bowl in the microwave or in a pot.
Pour the butter into a new bowl and mix in yeast, milk, and eggs.
Stir it together with sugar.
Sift flour and salt into the mixture.
Stir it well together; the dough should be quite soft.
Cover the bowl, for example, with a lid or a clean tea towel.
Let it rise for about 1 hour, preferably in a warm place.
Sprinkle flour on the kitchen counter and roll out the dough to a thickness of about 1 cm.
Cut out your donuts. If you don't have a cutter, use glasses or small bowls. They should be about 9-10 cm in diameter for the entire donut and make a hole in the middle. The hole should be about 2.5-3.5 cm in diameter.
The leftover dough can of course be rolled out again, so almost all of it can be used.
You can of course also cook the holes separately; they will end up looking like donut holes.
Place the cut-out donuts on a baking sheet lined with parchment paper. Let them rise for another 20-30 minutes with a clean tea towel over them.