3 cups sifted all-purpose flour, plus more for dusting
1 cup unsifted cake flour
1 tablespoon baking powder
1 1/2 teaspoon salt
1 teaspoon baking soda
1 teaspoon cinnamon
1 teaspoon freshly grated nutmeg
3/4 cup sugar
3 extra-large eggs, at room temperature
1 1/2 teaspoons pure vanilla extract
1 cup sour cream, at room temperature
1/4 cup plus 1 tablespoon solid vegetable shortening, melted
1/4 cup milk
Vegetable oil, for deep frying
Dark Chocolate Glaze or Vanilla Glaze
Chopped nuts, toasted coconut and sprinkles, for decorating (optional)
In a bowl, whisk both flours with the baking powder, salt, baking soda, cinnamon and nutmeg. In a large bowl, beat the sugar with the eggs until pale and thick. Beat in the vanilla.
In another large bowl, whisk the sour cream with the shortening and the milk. Beat the sour cream mixture into the eggs in 2 batches, alternating with the dry ingredients. Cover the bowl loosely with plastic wrap and refrigerate until chilled, at least 2 hours or overnight.
In a large, heavy skillet, heat 4 inches of vegetable oil to 370°. Line a rack with several paper towels.
Meanwhile, turn the dough out onto a floured surface. Roll out the dough 1/2 inch thick. Using a 2 1/2-inch doughnut cutter dipped in flour, cut out as many doughnuts as possible. Reroll the scraps once to cut out more doughnuts.
The recipe can be prepared through Step 2 and refrigerated overnight. The finished doughnuts can be made up to 4 hours ahead.