Simmer apple cider in a small saucepan over medium heat until reduced to about 1/2 cup, approximately 20-30 minutes. Set aside to cool.
In a large bowl, whisk together flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, whisk together the reduced apple cider, melted butter, brown sugar, granulated sugar, egg, vanilla extract, and buttermilk until well combined.
Add the wet ingredients to the dry ingredients and mix until just combined. Do not overmix.
Preheat oven to 350°F. Grease a donut pan. Fill each donut well about three-quarters full with batter. Bake for 10-12 minutes or until a toothpick comes out clean. Allow to cool slightly before removing from the pan.
Mix 1 cup granulated sugar and 1 teaspoon cinnamon in a shallow dish. While donuts are still warm, coat them in the sugar-cinnamon mixture.