Preheat the oven to 350˚F/175˚C.
Reduce cider: Simmer cider in a small saucepan for 15-20 minutes until it reduces to ½ cup.
Mix dry ingredients: Whisk together all-purpose flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt in a large bowl.
Mix wet ingredients: In a separate bowl, whisk together melted butter, applesauce, milk, both sugars, vanilla extract, apple cider vinegar, and the reduced apple cider.
Combine: Gently stir wet ingredients into dry until just combined. Avoid overmixing.
Pipe into pan: Grease a donut pan and pipe the batter about ¾ of the way into each cavity.
Bake: Bake for 10-11 minutes until the tops are lightly golden brown. Transfer to a cooling rack.
Cinnamon sugar coating: Mix cinnamon and sugar in a shallow bowl. Coat donuts by spraying with nonstick baking spray or brushing/dipping in melted butter, then rolling in cinnamon sugar. The oil/butter helps the coating stick. Enjoy while hot!