Reduce the Apple Cider: Pour the apple cider into a small saucepan over medium-high heat. Simmer until the liquid has reduced to exactly ½ cup. This should take about 10-15 minutes. Let it cool completely before using it in the batter.
Preheat and Prep: Preheat your oven to 350°F (175°C). Lightly grease a 12-count donut pan with non-stick cooking spray or a little bit of melted butter to ensure the donuts pop out easily after baking.
Mix the Dry Ingredients: In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, baking soda, cinnamon, nutmeg, and salt. Make sure there are no lumps in the flour for a smooth batter.
Combine the Wet Ingredients: In a separate medium bowl, whisk together the cooled reduced apple cider, egg, buttermilk, melted butter, and vanilla extract until well combined.
Create the Batter: Slowly pour the wet ingredients into the dry ingredients. Use a spatula to fold them together just until combined. Be careful not to overmix, as this can make the donuts tough.
Fill the Donut Pan: Spoon the batter into the prepared donut pan, filling each cavity about ¾ full. For a cleaner look, you can use a piping bag or a zip-top bag with the corner cut off to pipe the batter into the rings.
Bake the Donuts: Bake for 10 to 12 minutes, or until a toothpick inserted into the center comes out clean. Let the donuts cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
Glaze and Finish: While the donuts cool, whisk together the powdered sugar, maple syrup, and milk in a small bowl until smooth. Dip the top of each cooled donut into the maple glaze and place them back on the wire rack to set.