Add the apple cider to a small sauce pan set over medium heat. Bring to a simmer for 20 to 30 minutes and reduce the apple cider to about 1/4 cup. Set aside to cool.

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

In the bowl of a stand mixer, beat together the butter and sugar until light and creamy. Beat in the eggs one at a time until completely incorporated. Reduce the speed to low and add the apple cider and buttermilk, stirring just until combined.

Stir in the flour mixture just until the dough comes together.

Line two baking sheets with parchment paper and sprinkle with flour.

Place the dough on one baking sheet and flatten it out with your hands to about 1/2 inch thick.

Transfer the dough to the freezer for about 20 minutes.

Use a donut cutter to cut donuts and place them on the second baking sheet. Re-roll and cut out any scraps. Place the cut donuts in the refrigerator for 20 minutes.

Add enough oil or shortening to a deep sided pan to measure about 3 inches deep. Heat to 350 degrees. Line a plate with paper towels for draining the donuts.

Serve immediately.