Bring the apple cider to a boil in a medium saucepan and then lower the heat and simmer for about 15 to 20 minutes, until the cider reduces to ½ cup. Transfer the reduced cider to a bowl or measuring cup and allow it to cool in the refrigerator.

Combine the flour, baking powder, baking soda, salt, cinnamon, and nutmeg in a bowl.

Cream the butter and brown sugar together until light and fluffy using a stand mixer or a large bowl and an electric hand mixer. Add the eggs one at a time and pour in the reduced apple cider. Add the dry ingredients to the wet ingredients and mix well until combined. Grate the apple with a box grater right into the dough and continue to mix. Then, turn the dough out onto a lightly floured surface and knead by hand for a few minutes until the soft dough comes together. The dough should not be sticky (add a little flour if it is). Divide the dough into two disks and wrap each one with plastic wrap. Refrigerate the dough for 30 minutes.

Roll the dough out until it is 1 inch thick. Use a 3-inch round cookie or biscuit cutter to cut circles out of the dough. Then use a 1-inch round cookie cutter to cut a hole in the center of each circle. Gather the scraps into a ball and repeat with the remaining dough.

Pre-heat the air fryer to 360°F for 2 minutes.

Spray or brush the bottom of the air fryer basket with a little vegetable oil. Place 3 to 4 of the dough circles into the air fryer basket and let the dough rest in the (turned off) air fryer for 5 minutes to proof the dough. Then air-fry at 360°F for 5 minutes, turning over halfway through the cooking process. Repeat with the remaining doughnuts, letting each batch sit in the warm but turned off air fryer for 5 minutes before air-frying. (Don't forget to cook the holes too!)

Combine the sugar and cinnamon together and place it in a shallow dish. Brush all sides of the cooked doughnuts with some melted butter and then toss in the cinnamon sugar. Grab a cup of coffee and enjoy.