Preheat the oven to 350°F.
Reduce the apple cider by simmering it on low heat for 20-30 minutes until it reaches ¾ cup.
Whisk together the flour, granulated sugar, light brown sugar, baking powder, baking soda, cinnamon, and nutmeg in a large bowl.
Beat the butter and sugars in a stand mixer until creamy, then add the eggs one at a time, followed by the vanilla extract.
Gradually mix in the dry ingredients until just combined, being careful not to overmix.
If using, fold in the grated apple.
Spoon or pipe the batter into a specialized donut pan, filling each cavity about ⅔ full.
Bake for 12-15 minutes, rotating the pan halfway through, until the donuts are golden brown and a toothpick inserted comes out clean.
Allow the donuts to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
Dredge the warm donuts in a mixture of granulated sugar, cinnamon, and nutmeg to coat.