Simmer apple cider in a saucepan over medium heat until reduced to ½ cup (about 20 minutes). Let cool completely.
In a large bowl, whisk together flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, whisk together eggs, buttermilk, reduced cider, melted butter, and vanilla.
Pour wet ingredients into dry ingredients and stir until just combined. Cover and refrigerate overnight (or at least 2 hours).
Christmas morning: Preheat oven to 350°F. Grease two donut pans well. Spoon batter into donut cavities, filling about ¾ full.
Bake for 10-12 minutes until donuts spring back when touched. Let cool for 5 minutes, then brush with melted butter and roll in cinnamon-sugar mixture.