Reduce the Apple Cider: Pour 1 cup of apple cider into a small saucepan over medium heat. Simmer the cider until it has reduced to exactly 1/3 cup. This should take about 10-15 minutes. Set it aside to cool completely before using it in the batter.
Prepare Oven and Pan: Preheat your oven to 350°F (175°C). Lightly grease a 24-count mini-muffin tin with non-stick cooking spray or a little bit of melted butter to ensure the donut holes release easily after baking.
Whisk Dry Ingredients: In a large mixing bowl, whisk together the flour, sugar, baking powder, cinnamon, nutmeg, and salt. Make sure there are no large clumps of flour to ensure a smooth, even batter.
Combine Wet Ingredients: In a separate medium bowl, whisk together the egg, melted butter, buttermilk, vanilla extract, and the cooled, reduced apple cider. Mix until well combined and the color is consistent.
Mix the Batter: Slowly pour the wet ingredients into the dry ingredients. Use a spatula or wooden spoon to fold the mixture together just until no streaks of flour remain. Be careful not to overmix, as this can make the donut holes tough.
Fill and Bake: Spoon the batter into the prepared mini-muffin tin, filling each cup about 3/4 of the way full. Bake for 12 to 15 minutes, or until a toothpick inserted into the center comes out clean. Let them cool in the pan for 5 minutes before moving them to a wire rack.
Glaze the Donut Holes: While the donut holes are cooling, whisk together the powdered sugar, 2 tablespoons of cider, and cinnamon in a small bowl. Dip each warm donut hole into the glaze, turning to coat. Place them back on the wire rack to allow the glaze to set.