Reduce the Apple Cider: Pour the apple cider into a medium saucepan. Bring it to a gentle simmer over medium heat and cook until it reduces to about ¾ cup. Remove from the heat and let it cool slightly.
Prepare the Dry Ingredients: In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, cinnamon, nutmeg, and salt until evenly combined.
Mix the Wet Ingredients: In a separate bowl, whisk together the eggs, granulated sugar, brown sugar, melted butter, vanilla extract, and cooled reduced apple cider until smooth.
Combine the Batter: Gradually add the dry ingredients to the wet mixture. Gently stir with a spatula just until combined. Avoid overmixing, as this can make the donuts dense.
Fill the Donut Pan: Preheat the oven to 350°F. Lightly grease a 12-cavity donut pan. Spoon or pipe the batter evenly into the cavities, filling each about ¾ full.
Bake the Donuts: Bake for 10–12 minutes, or until the donuts are lightly golden and spring back when gently touched. Be careful not to overbake.
Prepare the Cinnamon Sugar: While the donuts bake, combine the granulated sugar and ground cinnamon in a shallow bowl. Mix well.
Coat the Donuts: Let the donuts cool for a few minutes until they're easy to handle. While they are still slightly warm, gently toss each donut in the cinnamon-sugar mixture until well coated.
Serve Warm: Transfer the finished apple cider donuts to a serving plate. Enjoy them warm with coffee, tea, or a glass of apple cider.