In a small saucepan over medium heat, bring the apple cider to a simmer. Reduce heat to low and simmer uncovered for 15-20 minutes or until the cider has reduced to 1/3 cup. Set aside to cool.
Preheat the oven to 400 degrees. Spray a donut pan with cooking spray and set aside.
In a medium mixing bowl combine the flour, baking powder, cinnamon, nutmeg, and salt.
In another medium mixing bowl cream the butter and sugar until smooth. Add in the egg and continue beating. Mix in half the flour mixture.
Stir in the milk and then add the remaining flour mixture. Stir until well combined then add in the apple cider. Mix until just combined.
Fill the donut pan 2/3 of the way full and put into the oven for 9-11 or until the donuts are golden brown. Remove from oven and put on a wire rack.
Combine the apple pie spice and sugar on a plate. Place the apple cider in a shallow bowl and dunk the top of sides of a donut into the apple cider then dip into the cinnamon and sugar mixture. Repeat with remaining donuts. Donuts will keep for 2-3 days.