Sift then measure flour; resift with baking powder, salt and nutmeg. Cream together sugar, butter and vanilla until light and fluffy. Add eggs one at a time, beating well after each addition. Blend in dry ingredients alternately with milk. Cover bowl. Chill three hours.
Preheat fat to 375 deg. F. Pat dough out on lightly floured board in 1/2 inch thickness. Cut with floured knife into 1 inch squares. Add few at a time to hot fat, frying 1-1/2 to two minutes a side or until browned. Drain on absorbent paper. Roll in icing sugar.