In a small pot, simmer apple cider over low heat. Reduce until 1/2 cup remains, about 15-20minutes. Remove from heat. Let cool for 10 minutes.
Preheat oven to 350 degrees F. Spray donut pan with nonstick cooking spray.
In a large bowl, whisk flour, baking soda, baking powder, cinnamon, apple pie spice and salt.
In a separate bowl, whisk butter, egg, sugars, milk and vanilla extract. Pour into dry ingredients. Add apple cider. Stir until smooth and combined. Spoon batter into donut pan, filling about halfway.
Bake for 10-12 minutes, or until tops are puffed and golden brown. Let cool for 2 minutes. Transfer to a wire rack to cool completely. Re-coat donut pan with nonstick spray. Fill and bake the remaining donut batter.
For the topping:
Prepare melted butter in a medium bowl. In a separate bowl, combine sugar, cinnamon and spice. Dunk donuts in butter, then roll generously in cinnamon-sugar topping.
* For an apple pie spice substitute (makes 1 teaspoon):
1/4 teaspoon ground cinnamon
1/4 teaspoon ground nutmeg
1/4 teaspoon ground allspice
1/4 teaspoon ground ginger
Donuts are best served immediately. Leftovers keep well covered tightly at room temperature for up to 2 days or in the refrigerator for up to 5 days.Adapted from Sally's Baking Addiction