Place 1 cup of apple cider in a small saucepan over medium-high heat. Simmer the cider until it has reduced to about 1/3 cup. This should take about 10-15 minutes. Let it cool completely before using it in the batter. This step is crucial for concentrated apple flavor.
Preheat your oven to 350°F (175°C). Lightly grease a 24-cup mini muffin tin with non-stick cooking spray or a little bit of melted butter to ensure the donut holes pop out easily after baking.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, 1 teaspoon of cinnamon, nutmeg, and salt. Make sure there are no large clumps so the batter stays light and airy.
In a separate medium bowl, whisk together the sugar, egg, melted butter, buttermilk, vanilla extract, and the cooled, reduced apple cider. Stir until the mixture is smooth and the sugar has started to dissolve.
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 donut holes tough instead of fluffy.
Spoon the batter into the prepared mini muffin tin, filling each cup about 3/4 full. Bake for 10 to 12 minutes, or until a toothpick inserted into the center comes out clean. Let them cool in the pan for 2-3 minutes.
While the donut holes are still warm, melt 4 tablespoons of butter in a small bowl. In another bowl, mix 1/2 cup of sugar with 1 tablespoon of cinnamon. Dip each donut hole quickly into the melted butter, then roll it in the cinnamon sugar until fully coated.