In a medium bowl or the bowl of a standmixer, combine the very warm milk, butter, flour, yeast, sugar, vanilla sugar, salt, and the egg.
Either using the standmixer with the dough hook attached, a handheld mixer, or your hands knead the dough for at least 5 minutes.
If the dough is too wet, add enough flour to make a uniform dough that does not stick to the bowl.
Let the dough rise until visibly increased in size (30 - 60 minutes).
On a lightly floured surface, roll out the dough.With a knife or pizza wheel, cut out squares or any shape you like.
In a pot, heat about 1 quart of lard to about 325˚F.
In small batches, fry the the squares until golden-brown on both sides.
With a slotted spoon, transfer the Schmalzgebäck to a cooling rack covered with paper towels.
Dust liberally with powdered sugar.
This German Schmalzgebäck is best when eaten fresh and hot.