Preheat oven to 350 degrees Farenheit. Spray your 6-cavity donut pan with non-stick spray and set aside. If using a silicone donut pan, place on a baking sheet and set aside.
In a bowl, whisk together your flour, baking powder, salt, cinnamon, and nutmeg. Set aside.
In a bowl or stand mixer, cream your butter, brown sugar, and granulated sugar on medium speed until light and fluffy, 3 to 4 minutes. Add eggs one at a time, and scrape the bowl after each addition to incorporate evenly. Add vanilla and beat together.
Add flour mixture on low speed. If using a hand mixer, add all of the flour mixture and mix on low speed until just incorporated. Add apple cider in a slow and steady stream while mixing on low speed. Batter will look fluffy and light colored. Scrape bowl to make sure there aren't any pockets of flour. If there are, use a spatula and fold batter together to combine.
Pipe or spoon batter into your donut pan until cavities are 2/3 filled, about 1/4" away from the top of the cavity.
Bake for 6 minutes then rotate. Bake for another 6 minutes or until golden brown. Toothpick inserted into the center of the thickest portion should come out clean.
In a bowl, combine the cinnamon, sugar, and salt. Let donuts cool upside down in the pans for 5 minutes on top of a cooling rack, and then unmold your donuts carefully. Liberally brush melted butter on top. Dredge each donut in your bowl of cinnamon sugar while they're still warm. Enjoy immediately or place in an air tight container once they're cooled down to room temperature.