In a small saucepan on high heat bring the apple cider to a boil. Boil for about 15 to 20 minutes until reduced to one cup. Let cool completely.
In a large bowl whisk together the all-purpose flour, dark brown sugar, baking soda, powder, apple pie spice, fresh ground nutmeg, and salt.
In a small bowl whisk together the melted butter, eggs, and cooled apple cider.
Pour the wet ingredients into the dry ingredients and stir just until combined and all the flour mixture is moistened.
Cover and refrigerate for at least an hour.
Heat the vegetable oil in a dutch oven or large pot over medium-high heat to 375 degrees F. Watch closely and adjust as needed to make sure it doesn’t overheat. Or use an electric deep fryer.
Line a baking sheet with paper towels set aside.
In a paper bag or a small bowl mix together the granulated sugar, fresh ground nutmeg, and ground cinnamon. Set aside.
Divide the dough in half, working with one half at a time place it on a floured surface. Pat into 1/2 inch thick round. Place the remaining half of the dough back into the fridge. Using a doughnut cutter or a 3 inch round cutter and a 1 inch round cutter for the hole, cut into rounds.
Working in batches carefully slide the donuts into the heated oil. Cook on the first side for at least one minute, at this point they should be floating. Flip and fry about another 1 1/2 minutes longer until evenly golden brown. Keep an eye on the temperature of the oil. It can drop and rise quickly.
Transfer to the paper towel-lined baking sheet. Let cool about 1 minute, place the warm donut into the cinnamon-sugar mixture, and shake to coat evenly. If using a bowl roll the donut in the mixture.