Mix the flour, baking powder, nutmeg, and salt. Beat the fat into a cream with half of the sugar, beating until the mixture is light. Beat the eggs into a light foam, gradually adding the remaining sugar, beating well after each addition.
Gradually incorporate the eggs into the fat and sugar mixture and add the vanilla. Incorporate the dry ingredients, alternating with the milk. The dough should be soft, but not too sticky. Cover and refrigerate for at least one hour. Roll out with a rolling pin, on a floured board, to the desired thickness. Cut out with a floured beignet cutter. Cook 3 or 4 at a time, in deep frying oil. Drain well on both sides on absorbent paper. The beignets are more flavorful if reheated in the oven before serving. They can also be frozen and thawed in a slow oven at serving time. Dust with powdered sugar.