Apple Cider Doughnuts

Using a mixer, beat together sugar and butter until mixture is pale and fluffy, about four to six minutes. Add eggs, one at a time, and continue beating after each. In a medium-size bowl, whisk together flour, salt, baking powder, baking soda, cinnamon, and nutmeg, and set aside.   Pour buttermilk, boiled cider, and vanilla into sugar-butter-egg mixture and mix well. (It’s OK if the mixture looks curdled.) Add flour mixture and combine gently just until fully moistened.   Line two baking sheets with parchment paper and dust generously with flour. Turn dough out onto one baking sheet and pat gently into three-quarter-inch thickness. Sprinkle dough with additional flour, cover with plastic wrap, and place in freezer for 10 minutes. Remove dough from the freezer. Use a lightly floured three-inch doughnut cutter (or two concentric biscuit cutters) to cut out about 18 doughnuts with holes. (For more doughnuts, gather scraps, chill the dough and roll again.) Place cut doughnuts on the second baking sheet; then transfer to the freezer for five minutes.   Line a plate with a few layers of paper towels and set nearby. In a Dutch oven or large pot, heat three inches of oil to 370°F. (Test with an instant-read thermometer.) Drop three or four doughnuts into the oil, taking care not to crowd the pan. Cook until brown on one side, about 1 minute; then flip and cook until brown on the other side, about one minute longer. Repeat with the remaining dough. (If you find that the dough is getting too soft as you work your way through the batches, return to the freezer for 10 minutes.) When doughnuts are cool enough to handle but still warm, sprinkle with cinnamon sugar or confectioners’ sugar. Serve immediately.