Step 1

Reduce the apple cider. Bring 2 1/2 cups apple cider to a boil in a large frying pan over medium-high heat. Boil until reduced to 1/3 cup and syrupy, about 10 minutes. (If you reduce it by too much, just add enough water to get back to 1/3 cup.) Meanwhile, cut 6 tablespoons unsalted butter into 6 pieces. Mix the dry ingredients.

Step 2

Mix the dry ingredients. Place 3 1/2 cups all-purpose flour, 1/2 teaspoon of the ground cinnamon, 2 teaspoons baking powder (4 teaspoons if you plan to let the dough chill overnight), 1 teaspoon kosher salt, 1/2 teaspoon baking soda, and 1/2 teaspoon ground nutmeg in a large bowl and whisk to combine.

Step 3

Add the butter and sugar. When the cider is ready, remove the pan from the heat. Add the butter and whisk until melted and combined. Add 1/2 cup packed brown sugar and whisk until melted. Scrape the mixture into a medium bowl.

Step 4

Add the remaining wet ingredients. Add 1/2 cup unsweetened applesauce, 1/3 cup cold buttermilk or kefir, and 2 cold large eggs. Whisk until smooth.

Step 5

Mix the dough. Scrape the cider mixture into the flour mixture and stir with a rubber spatula until a sticky dough forms. Do not overmix.

Step 6

Chill the dough and make the cinnamon sugar. Cover the bowl and refrigerate 1 hour (or overnight if you used 4 teaspoons baking powder). Meanwhile, place the remaining 2 1/2 teaspoons ground cinnamon and 1 cup granulated sugar in a wide, shallow bowl or pie plate and stir to combine.

Step 7

Heat the oil and prepare for frying. Fill a Dutch oven or large, heavy-bottomed pot with 2 quarts vegetable oil (at least 1 1/2 inches of oil) and clip on a deep-fry thermometer. Heat the oil over medium-high heat until 350ºF. Meanwhile, fit a wire rack onto a baking sheet. Dust a second baking sheet lightly with flour. Cut out the doughnuts.

Step 8

Roll out the dough. Generously flour a work surface, then transfer the dough (it will not be smooth) onto it. Generously dust the top of the dough and a rolling pin with flour. Roll the dough out until 1/2-inch thick (about a 12-inch wide round).

Step 9

Cut out doughnuts. Cut doughnuts out with a floured doughnut cutter (or use 2 round cutters about 3 and 1-inch in diameter). The dough may be a little sticky, and it’s okay to twist the cutters as you push them in to get a clean cut. Transfer the doughnuts and doughnut holes to the floured baking sheet. Gather the scraps and form them into a ball, then roll out again until 1/2-inch thick. Repeat cutting until you have at least 12 doughnuts and 12 doughnut holes. If the oil is not ready yet, place the baking sheet in the refrigerator.

Step 10

Fry the first batch. Fry in batches of 4 doughnuts. Gently place the doughnuts in the oil and fry, flipping once, until puffed and golden brown, about 1 minute per side. Use tongs or chopsticks to gently remove the doughnuts from the hot oil, hold them over the pot for a few seconds to drain off the excess oil, and place on the wire rack.

Step 11

Roll the doughnuts in cinnamon sugar. Immediately place the doughnuts one at a time in the reserved cinnamon sugar and toss until well-coated, sprinkling some of the sugar over the doughnut and making sure the sides are well coated. Return to the wire rack.

Step 12

Fry the remaining doughnuts. Repeat with frying the remaining doughnuts, adjusting the heat as needed to maintain an oil temperature of 350ºF and tossing each batch in the cinnamon sugar immediately after they are fried.

Step 13

Fry the doughnut holes. Fry the doughnut holes in 2 batches, about 1 minute per side, and coat in cinnamon sugar.