In a small saucepan, bring the apple cider to a boil. Reduce heat and simmer until it reduces to about 1/4 cup. Let cool.
Preheat your oven to 350°F (175°C). Grease a donut pan.
In a large bowl, whisk together granulated sugar, brown sugar, and melted butter. Add eggs and vanilla extract, mixing well.
In another bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Gradually add the dry ingredients to the wet ingredients, alternating with buttermilk, beginning and ending with the dry ingredients. Mix until just combined.
Stir in the reduced apple cider.
Spoon the batter into the prepared donut pan, filling each cavity about 3/4 full.
Bake for 10-12 minutes, or until a toothpick inserted into the center comes out clean.
Let the donuts cool in the pan for a few minutes before transferring to a wire rack.
While the donuts are still warm, mix the coating sugar and cinnamon in a shallow bowl. Dip each donut in the mixture to coat.
Serve warm or at room temperature.