Sift the flour into a bowl. In another bowl mix together the milk and egg yolks with a little bit of salt. Add the milk mixture to the flour and blend to a smooth dough.
Saute the bread in the butter over moderate heat until golden. Sprinkle the bread over the dough. Pour on the goose fat and let the mixture mellow 1 hour. Blend the bread into the dough. Beat 2 egg whites until stiff and fold them into the dough.
Soak a tea towel in water, squeeze it dry and line a sieve with it. Add the dough and pull the cloth up around the dough and tie it off immediately above dough. Transfer the wrapped dough to a pot of simmering water with a rack and poach it for 1 hour. Transfer it to a platter, let it cool a little, and then untie it and cut the dumpling with a thread into slices.