In a large glass bowl, cream the sugar, eggs, vanilla and butter.
Combine the flour and baking powder. Alternate adding the flour mixture and the milk in the creamed ingredients.
Roll out dough in flour and sugar, and cut desired size. Drop in hot oil turning once when brown. Do not crowd the doughnuts or add too many at a time into the oil. This has a tendency to cool the oil too fast and make the pastries greasy.