Pour your apple cider (not apple cider vinegar) into a small saucepan and heat over medium heat until simmer. Simmer for 15-20 minutes, or until reduced down to ½ cup. Note: if you reduce it down too far, just add more apple cider or water to make it equal ½ cup. Leave the hot apple cider to cool for at least 1 hour, or until at room temperature.
Preheat oven to 350° and grease a donut pan. In a mixing bowl, stir together the flours, cinnamon, baking powder, baking soda, ginger, nutmeg, and salt until well combined. Set aside.
In a separate bowl, whisk together the brown sugar, milk, oil, egg, applesauce, and vanilla extract until smooth. Add the dry ingredients and whisk until well-combined.
Transfer the batter to a large ziplock bag, cut the corner off to make a small opening, then pipe the batter into the donut pan to form 16 donuts. They should be about ¾ full. Bake in the preheated oven for 8-10 minutes, until risen and golden brown.
While your donuts are baking, stir together the cinnamon and sugar in a shallow bowl.
Allow the donuts to cool in the pan, then remove and transfer them to a cooling rack with a towel or baking sheet underneath to prevent a cinnamon sugar mess!
Brush each donut with butter on all sides, then dip in the cinnamon sugar mixture, coating on all sides. Place each donut back on the cooling rack. Serve or store at room temperature for up to 3 days!