Reduce the cider. Add the apple cider to a small saucepan and simmer over medium heat until it reduces to about 1/2 cup, 10–15 minutes. Cool slightly. This is your flavor bomb.
Preheat and prep. Heat oven to 350°F (175°C). Grease a mini muffin pan or a donut hole pan. No pan? A regular muffin pan works—just fill each cup 1/3 full.
Mix dry ingredients. In a bowl, whisk flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Keep it airy for a light crumb.
Mix wet ingredients. In another bowl, whisk granulated sugar, brown sugar, egg, melted butter, buttermilk, vanilla, and 1/4 cup of the reduced cider. Save remaining cider for glazing or to adjust batter thickness.
Combine gently. Add dry to wet and fold just until combined. If batter seems too thick, add 1–2 teaspoons more reduced cider. Do not overmix or you'll get rubbery bites.
Fill the pan. Spoon or pipe batter into the wells, about 3/4 full. Consistency should be thick but scoopable.
Bake. Bake 9–12 minutes for mini muffin size (12–15 for larger). They're done when the tops spring back and a toothpick comes out clean.
Coat while warm. Let cool 2 minutes, then pop them out. Brush or dip each in melted butter and roll in the cinnamon-sugar mixture. Work in batches so the sugar sticks well.
Optional glaze. Whisk powdered sugar with 1–2 tbsp reduced cider until smooth. Drizzle over sugared donut holes once set. Extra? Not necessary. Worth it? Absolutely.