Before you begin, you will need to reduce the apple cider. Add apple cider to a small saucepan and 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 for about 10 minutes.
Preheat oven to 350°F. Spray a donut pan with cooking spray and set aside.
In a large bowl, whisk together the flour, baking powder, cinnamon, nutmeg and salt; 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.
Add the wet ingredients in with the dry ingredients; stir until just incorporated. Do NOT over mix or donuts will be tough.
Spoon the batter into a ziploc bag and snip off one corner. This makes it much easier to add batter into the donut wells. Add batter into prepared pan about 3/4 to the top of each donut well. Alternatively, you can spoon the batter into the donut cavities.
Bake donuts 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 carefully remove them from the pan and place on a wire rack to cool until they are warm to the touch, but you are 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 and bottoms into the melted butter and then quickly into the cinnamon sugar mixture. Repeat for the entire batch of donuts.