Preheat oven to 350°. Spray a donut pan with cooking spray and set aside.
Before you begin, you will need to reduce the apple cider. Pour apple cider in a small saucepan a simmer on low-medium heat for 15-20 minutes or until the cider reduces down to 3/4 cup. Once it is reduced, set it aside to cool.
In a large bowl, whisk together the flour, baking powder, pinch of salt, cinnamon and nutmeg and set aside.
In a separate bowl, mix the melted butter and sugars together until smooth. Add in the eggs and vanilla and stir until completely combined. Pour in the buttermilk and apple cider and mix until smooth. Stir in the flour mixture and mix until just incorporated. Do not over mix or donuts will be tough.
Pour the batter into a ziploc bag and snip off one corner. This makes it much easier to pour into the donut wells. Pour batter into prepared pan about 3/4 to the top of each well. Bake for 14-15 minutes or until the tops are firm and spring back slightly when you touch them. Do not over bake or you will have dry donuts.
When done, remove donuts from the oven and let them cool in the pan for 5 minutes then remove them carefully and place on a wire rack to cool until they are warm to the touch so you are able to handle them. While they are cooling, get your butter + cinnamon sugar topping ready.
In a small bowl, melt butter in the microwave. Set aside.
In a separate bowl, mix together the cinnamon and sugar. Set aside.
Once donuts are cool enough to be handled, dip the tops into the melted butter and then quickly into the cinnamon sugar mixture. Repeat for the entire batch of donuts.
These Apple Cider Donuts are best served fresh the same day, but will stay soft for up to 2 days stored in an airtight container. If they get a bit firm, you can reheat in the microwave for a few seconds to soften them up and they are good as new.