Pour the apple cider into a large frying pan and bring to a boil over medium-high heat.

Cook until the liquid reduces to about ⅓ cup and becomes syrupy, which should take around 10 minutes.

While the cider reduces, cut the butter into six pieces for easier melting.

Once the cider is ready, remove the pan from the heat, add the butter, and whisk until fully melted and combined.

Add the brown sugar and whisk until it is melted as well.

Scrape this syrupy mixture into a medium mixing bowl.

Add the unsweetened applesauce, cold buttermilk or kefir, and cold eggs to the bowl with the apple cider syrup mixture.

Whisk everything together until smooth.

Using cold eggs and buttermilk helps the dough stay tender and results in fluffier donuts.

In a separate large bowl, whisk together the flour, ½ teaspoon ground cinnamon, baking powder, kosher salt, baking soda, and ground nutmeg.

Scrape the wet cider mixture into the bowl with the dry ingredients.

Stir gently with a rubber spatula until a sticky dough forms, but be careful not to overmix.

Cover the bowl and refrigerate the dough for at least 1 hour (or overnight for a more developed flavor if you used extra baking powder).

While the dough chills, combine the remaining 2 ½ teaspoons of ground cinnamon with 1 cup granulated sugar in a wide, shallow bowl or pie plate and mix well.

Prep a wire rack by placing it over a baking sheet and lightly dust another baking sheet with flour.

Once the dough is chilled, generously flour your work surface and a rolling pin.

Transfer the sticky dough onto the floured surface and roll it out to ½-inch thickness.

Cut out donuts using a floured donut cutter or two round cutters.

Place the donuts and holes on the floured baking sheet.

Gather scraps, reroll, and cut again until you have at least 12 donuts and 12 holes.

Chill the cut donuts in the refrigerator if the oil isn’t hot yet.

Pour the vegetable oil into a large Dutch oven or heavy-bottomed pot to a depth of at least 1 ½ inches and clip on a thermometer.

Heat the oil over medium-high heat to 350ºF.

Working in batches of four, gently lower the shaped donuts into the hot oil.

Fry for about 1 minute per side, flipping once, until puffed and golden brown.

Remove the fried donuts with tongs or chopsticks, let excess oil drain briefly over the pot, and then transfer them to the wire rack.

Maintain the oil temperature at 350ºF throughout frying.

Fry the donut holes in 2 batches for about 1 minute per side.

While the donuts are still warm, immediately coat each one in the prepared cinnamon sugar.

Return coated donuts to the wire rack to cool slightly before serving.

Repeat with all of the donuts and donut holes, adjusting the cinnamon sugar as needed.

Toss the donuts while they’re still hot so the sugar really sticks for a crunchy, aromatic crust.