Step 1: Reduce the Apple Cider: Place 1.5 cups of apple cider in a small saucepan over medium heat. Simmer until the liquid has reduced to exactly 1/2 cup. This should take about 10 to 15 minutes. Set it aside to cool completely before adding it to the batter.
Step 2: Prepare the Oven and Pan: Preheat your oven to 350°F (175°C). Generously grease a 12-count donut pan with non-stick cooking spray or a light coating of melted butter to ensure easy removal.
Step 3: Mix the Dry Ingredients: In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, ground cinnamon, salt, and nutmeg until well combined and free of lumps.
Step 4: Combine the Wet Ingredients: In a separate medium bowl, whisk the egg, melted butter, vanilla extract, and the cooled 1/2 cup of reduced apple cider until the mixture is smooth.
Step 5: Fold the Batter: Pour the wet ingredients into the dry ingredients. Use a spatula to gently fold the mixture together until just combined. Be careful not to overmix, as this can make the donuts tough.
Step 6: Bake the Donuts: Spoon the batter into the prepared donut pan, filling each cavity about three-quarters full. Bake for 12 to 15 minutes, or until the tops spring back when lightly touched. Let them cool in the pan for 5 minutes before transferring to a wire rack.
Step 7: Prepare the Maple Glaze: In a small bowl, whisk together the powdered sugar, maple syrup, and enough milk or cider to reach a thick but pourable consistency. Dip the tops of the cooled donuts into the glaze and set them back on the wire rack to harden.