01 - Preheat the oven to 350°F and lightly grease a standard donut pan.
02 - Simmer apple cider in a small saucepan over medium heat until reduced to ½ cup, approximately 10 to 15 minutes. Allow to cool.
03 - Whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg in a medium bowl.
04 - In a large bowl, whisk melted butter, eggs, granulated sugar, and brown sugar until smooth. Stir in reduced cider, milk, and vanilla extract.
05 - Add the dry mixture to the wet ingredients and stir gently until just combined, avoiding overmixing.
06 - Spoon or pipe batter evenly into donut pan cavities, filling each approximately three-quarters full.
07 - Bake for 10 to 12 minutes until donuts spring back when lightly pressed.
08 - Let donuts cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
09 - Combine sugar and cinnamon in a shallow dish. Brush each donut with melted butter, then coat with cinnamon-sugar mixture.
10 - Serve donuts warm or at room temperature.