Reduce the Apple Cider: Pour the 1 1/2 cups of apple cider into a small saucepan over medium heat. Simmer until the liquid has reduced to exactly 1/2 cup. This usually takes about 15-20 minutes. Set it aside to cool slightly before using.
Preheat and Prepare: Preheat your oven to 350°F (175°C). Lightly grease two standard 6-cavity donut pans with non-stick cooking spray or a light coating of butter so the donuts release easily after baking.
Mix the Dry Ingredients: In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, cinnamon, nutmeg, and salt. Ensure there are no large lumps in the mixture.
Combine the Wet Ingredients: In a separate medium bowl, whisk together the egg, melted butter, milk, vanilla extract, and the cooled, reduced apple cider. Mix until well combined.
Create the Batter: Gently pour the wet ingredients into the dry ingredients. Use a spatula to fold the mixture together until just combined. Be careful not to overmix, as this can make the donuts tough.
Fill the Donut Pans: Spoon the batter into the prepared donut pans, filling each cavity about 3/4 full. For a cleaner look, you can use a piping bag or a plastic storage bag with the corner snipped off to pipe the batter into the rings.
Bake the Donuts: Bake for 12 to 15 minutes, or until the donuts are springy to the touch and a toothpick inserted comes out clean. Allow them to cool in the pan for 5 minutes before transferring to a wire rack.
Prepare the Maple Glaze: In a small bowl, whisk together the powdered sugar, maple syrup, and enough milk or cider to reach your desired consistency. It should be thick enough to coat the donut but thin enough to dip.
Glaze and Serve: While the donuts are still slightly warm, dip the top of each donut into the maple glaze. Place them back on the wire rack to let the glaze set for a few minutes before serving.