How to Make It
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.