01 - Simmer apple cider in a small saucepan over medium heat until reduced to half a cup, about 10 to 15 minutes. Allow to cool completely.
02 - Preheat oven to 350°F and grease two standard donut pans thoroughly.
03 - Whisk together flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt in a large bowl.
04 - In a separate bowl, whisk eggs, milk, melted butter, cooled reduced apple cider, and vanilla extract until smooth.
05 - Gently fold wet ingredients into dry mix until just combined, taking care not to overmix.
06 - Spoon or pipe batter evenly into donut pan cavities, filling each about two-thirds full.
07 - Bake for 12 to 15 minutes, until donuts spring back when pressed and a toothpick inserted comes out clean.
08 - Let donuts rest in pans for 5 minutes before transferring to a wire rack to cool completely.
09 - Combine sugar and cinnamon in a shallow bowl for coating.
10 - While still slightly warm, brush each donut with melted butter, then toss in cinnamon-sugar mixture until evenly coated.