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.