1. In a medium bowl, soft together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Add the sugar and stir the dry ingredients with a whisk until combined.
2. In a medium bowl, whisk together the buttermilk, melted butter, egg, and vanilla until blended. Make a well in the center of the flour mixture and pour the buttermilk mixture into it. Using a rubber spatula, stir until the moxture forms a soft, moist dough. Dust a work surface with flour. Scrape the dough onto the work surface and lightly sprinkle the top of the dough with flour. Gather the dough into a ball and knead it gently 5 or 6 times, or until smooth. Roll or pat the dough into a round roughly 10 inches in diameter and 1/2 inch thick. Transfer the round to a baking sheet, cover it with plastic wrap, and place it in the freezer for 15 minutes, or until firm.
3. Using a 3-inch doughnut cutter (or a 3-inch round biscuit cutter and a 3/4-inch cutter or pastry tip for the hole), cut out 7 doughnuts and holes from the dough. Gather the scraps together, reroll 1/2-inch thick, and cut out 3 more doughnuts and as many holes as possible. Place the doughnuts and holes on a baking sheet or 2 plates, cover with plastic wrap, and refrigerate while heating the oil for frying.
4. Pour the oil into a deep-fat fryer or large straight-sided saucepan to a depth of 2 to 3 inches. heat the oil to 370 degrees F. Line a baking sheet with paper towels.
5. Fry the doughnuts and holes in small batches, turning once, for 2 to 3 minutes, or until golden brown. Using a slotted spoon, transfer to the paper towels to drain, then place on a wire rack to cool completely.
6. When the doughnuts and holes are completely cool, place the confectioners' sugar in a medium bowl. Generously dredge the doughnuts and holes in the sugar, shaking off the excess. Serve the same day.
Diner Desserts (Chronicle Books, 2000) By Tish Boyle, Photographs by Clark Irey