Baked Sweet Potato Doughnuts

Make the doughnuts

1. Prick sweet potato all over with a fork and cook in a microwave at high power until tender, 8 to 10 minutes. Let sweet potato cool, then peel and puree; you should have about 1 cup.

2. Heat butter in a small skillet over moderate heat until nutty and lightly browned, about 4 minutes. Scrape browned butter and solids into a small bowl and let cool.

3. Add milk to skillet and heat until just warm, about 105°F. Pour warm milk into bowl of a standing electric mixer fitted with dough hook. Add yeast and let stand for 5 minutes. Add granulated sugar, light brown sugar, salt, vanilla seeds, nutmeg, and rum and beat on low speed. Add sweet potato puree, browned butter and solids, egg, and egg yolks and beat until combined. With mixer running on low speed, gradually add bread flour, then increase to medium speed and beat until dough is evenly moistened, 1 to 2 minutes. Increase speed to moderately high and beat until a soft dough forms, about 5 minutes. Gather dough into a ball and transfer to a buttered bowl. Cover and let rise in a draft-free place for 1 hour.

4. Punch down dough and let stand for 5 minutes. Roll out dough on a lightly floured surface to 1/2 inch thickness. Using a 2 3/4-inch round cutter, stamp out as many rounds as possible. Using a smaller (1-inch) round cutter, stamp out center of each round. Transfer doughnuts and holes to 2 parchment paper–lined baking sheets. Cover loosely with plastic wrap and let doughnuts and holes rise in a warm place for 1 hour.

5. Preheat oven to 400°F and position racks in upper and lower thirds of oven. Bake holes for 8 to 10 minutes and doughnuts for 15 to 20 minutes, until risen and golden.

Make the topping

1. In a small bowl, combine sugar and cinnamon. Put half of the hot doughnuts in a large bowl and drizzle with half of the melted butter; toss and turn to coat. Sprinkle with half of the cinnamon sugar and toss and turn until evenly coated. Repeat with remaining doughnuts, butter and cinnamon sugar. Transfer doughnuts to a platter; serve.