Preheat oven to 350° degrees F. Liberally grease two 6-cavity donut pans or a 12-cavity muffin pan with cooking spray and set aside.
Add the apple cider to a small saucepan over medium heat. Bring to a boil, then lower the heat to medium-low and simmer until reduced by half, about 5 minutes. You should now have 1/2 cup of apple cider. Set aside.
In the bowl of a stand mixer, cream together the butter and sugars with the paddle attachment until fluffy and creamy, about 3 minutes. Add in the eggs, one at a time, mixing well after each addition, followed by the vanilla extract. Add in the flour, baking powder, salt, cinnamon and nutmeg and mix in slowly until incorporated. Lastly, slowly stream in the reduced apple cider until batter comes together cohesively.
Spoon the batter into a piping bag and pipe the batter into the donut tins, filling about 2/3 of the way full. Or, spoon into the muffin tin filling about 2/3 of the way full. Bake the donut pans for about 12-15 minutes or until a toothpick inserted near the center comes out clean. If baking muffins, bake for about 15-20 minutes or until a toothpick comes out clean.
While the donuts bake, whisk together the remaining granulated white sugar and cinnamon in a small bowl. Once the donuts are finished baking, allow them to cool in the pan for about 5-10 minutes, then carefully invert them onto a wire rack. Let cool for another 5 or so minutes, then dip into the melted butter and dredge into the cinnamon sugar mixture to coat the donut exterior in cinnamon sugar. Serve immediately. It's best to dredge the donuts when they're cooled off some as when you dip and dredge when they're super hot, they're really fragile.