Sift together sugar, baking powder, cinnamon, nutmeg, salt, and flour.
Beat eggs thoroughly, then stir into dry ingredients. Add the milk and melted butter. Roll about 1/2 inch thick on a floured board and cut with a doughnut cutter.
Fry several at a time in 375 degrees F fat until nicely browned.
Drain on paper towels. Dust with granulated or confectioners' sugar.