Whisk the flour, baking powder, salt, cinnamon and nutmeg. Set aside.
In a large bowl, lightly beat yolks on medium speed. Gradually add sugar, beating until pale and slightly thickened, about 3 minutes. Mix in butter. Add flour mixture alternately with milk, stirring with wooden spoon until combined.
On well-floured surface, with floured rolling pin, roll dough into 1/2 inch thickness. Let rest 15 minutes.
Meanwhile, heat oil to 365º (a cube of bread will be browned and crisp after 1 minute) in a heavy saucepan over medium-high heat.
Cut into doughnuts with 2 3/4-inch round cutter along with a 3/4-inch round cutter for the centers. Gather scraps and re-roll if needed.
Coating – place cinnamon-sugar in a small bowl.
Carefully slip the doughnuts and the doughnut holes, 3 or 4 at a time into the hot oil. Fry until golden about 2 to 3 minutes per batch. Drain on paper towels, then transfer while still warm to the cinnamon sugar mix, coat all over. Serve warm.