Reduce the Apple Cider
In a small saucepan, bring the apple cider to a simmer over medium heat. Allow it to reduce for about 10-15 minutes, until it thickens to about ½ cup. Set aside to cool.
Preheat the Oven
Preheat your oven to 350°F (175°C). Grease a donut pan with cooking spray or butter.
Mix the Dry Ingredients
In a large bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Mix the Wet Ingredients
In another bowl, beat the eggs and sugar together until smooth. Add the cooled apple cider, melted butter, milk, and vanilla extract. Mix until well combined.
Combine Wet and Dry Ingredients
Gradually fold the dry ingredients into the wet ingredients, mixing until just combined.
Fill the Donut Pan
Spoon the batter into the donut pan, filling each cavity about ¾ full.
Bake the Donuts
Bake for 12-15 minutes, or until a toothpick inserted into the center of a donut comes out clean. Let the donuts cool for a few minutes in the pan before transferring them to a wire rack.
Coat the Donuts in Cinnamon Sugar
While the donuts cool, combine the sugar and cinnamon in a shallow bowl. Brush the slightly cooled donuts with melted butter and roll them in the cinnamon-sugar mixture until fully coated.