01 - Preheat oven to 350°F. Grease two standard donut pans thoroughly.
02 - Simmer apple cider in a small saucepan over medium heat until reduced to 1/2 cup, approximately 10 to 12 minutes. Allow to cool.
03 - In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, ground cinnamon, ground nutmeg, granulated sugar, and light brown sugar until evenly combined.
04 - In a separate bowl, whisk together the cooled reduced apple cider, eggs, unsweetened applesauce, vegetable oil, and vanilla extract until smooth.
05 - Add wet mixture to dry ingredients and stir gently just until the batter is combined, ensuring not to overmix.
06 - Spoon or pipe the batter evenly into the prepared donut pans, filling each cavity approximately three-quarters full.
07 - Bake for 10 to 12 minutes, or until donuts spring back when lightly pressed.
08 - Let donuts cool in the pan for 5 minutes, then transfer to a wire rack.
09 - In a shallow bowl, mix together granulated sugar and ground cinnamon.
10 - Brush each donut with melted unsalted butter and roll in the cinnamon sugar mixture until fully coated.