Add the apple cider to a saucepan and heat on medium-high and cook, stirring frequently, until the mixture is only about 2 tablespoons and a thick syrup.
In a mixing bowl, beat together the butter and sugar until the mixture becomes light and fluffy - about 2 minutes.
Beat in an egg for about a minute.
Add in the cider and beat until fully incorporated.
Stir in the flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Mix until just combined.
Drizzle in the buttermilk and stir until just combined.
Line a baking sheet with parchment paper and put the dough onto the sheet. Top with another sheet of parchment paper. Roll out until about ¼-inch to ½-inch thick.
Place in the refrigerator for about an hour, or until the dough doesn't stick to the parchment so much.
Quickly take off the top parchment - it works best when you take it off like a band-aid.
Flour a flat surface, then place the exposed half of dough onto the flour then remove the other parchment paper.
Flour a doughnut cutter and cut out your dough.
Heat at least three inches of oil to 375 degrees F.