01 - Preheat oven to 350°F. Lightly grease a standard donut pan.
02 - Simmer apple cider in a small saucepan over medium heat until reduced to approximately ½ cup, about 10 to 15 minutes. Let cool.
03 - Whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg in a medium bowl.
04 - Whisk melted butter, eggs, granulated sugar, and brown sugar in a large bowl until smooth. Add reduced apple cider, milk, and vanilla extract, mixing until combined.
05 - Add dry mixture to wet ingredients and stir gently until just combined, avoiding overmixing.
06 - Spoon or pipe batter evenly into donut pan cavities, filling each about ¾ 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 before transferring to a wire rack.
09 - Combine sugar and cinnamon in a shallow bowl. Brush donuts with melted butter then dip into the cinnamon-sugar mixture to coat.
10 - Serve donuts warm or at room temperature.