Apple Cider Doughnuts

Bring apple cider to a boil over medium-high heat in a small Dutch oven. Boil until cider is reduced to 1 cup, about 40 minutes. Remove from heat. Let cool to room temperature.

Beat butter, ½ cup sugar, and vanilla in a large bowl with a mixer at medium speed until combined. Add egg, beating until thick and pale, about 2 minutes. Beat in sour cream.

Whisk together flour, baking powder, ¼ teaspoon Apple Pie Spice, and salt in a medium bowl. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined. Add apple, beating just until combined. Wrap dough in plastic wrap. (Dough will be slightly sticky.) Refrigerate for 30 minutes.

Knead dough gently 3 or 4 times on a lightly floured surface. Roll dough to ½-inch thick. Using a 3-inch doughnut cutter dipped in flour, cut dough, rerolling scraps as necessary. Fill a cast-iron Dutch oven halfway full with oil, and heat over medium until a deep-fry thermometer registers 350°.

Add doughnuts to hot oil working in small batches; fry until golden brown, about 1½ minutes per side. Fry doughnut holes for about 1 minute. Remove using a slotted spoon, and let drain on paper towels. Let cool slightly.

Combine remaining 1 cup sugar and remaining 1 teaspoon Apple Pie Spice in a large bowl. Dip doughnuts and doughnut holes in sugar mixture, shaking off excess. Drizzle with apple cider syrup.