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