In a saucepan over medium heat, simmer the apple cider until reduced to 1/2 cup, about 10-15 minutes. Let cool.
Preheat the oven to 350°F (175°C) and grease a donut pan.
In a mixing bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, beat the melted butter and brown sugar until combined.
Add the eggs, vanilla extract, and reduced apple cider, mixing until smooth.
Gradually add the dry ingredients, alternating with the milk, and mix until just combined.
Spoon the batter into the donut pan, filling each cavity about 3/4 full.
Bake for 12-15 minutes, or until a toothpick inserted in the center comes out clean.
Let the donuts cool for 5 minutes before transferring to a cooling rack.
In a small bowl, mix the granulated sugar and cinnamon for coating.
Brush each donut lightly with melted butter and roll in the cinnamon-sugar mixture.
Serve warm and enjoy!