In a small saucepan, simmer the apple cider over medium-low heat for about 15 minutes. Reducing it will bring out a strong, vibrant flavor for the donuts. Take ½ cup of the mixture and place it in the refrigerator to cool.
Preheat the oven to 350°F and grease your donut pan. While the oven is heating, mix together all of your dry ingredients together in a large bowl. Set aside. In a medium bowl, mix together your egg, butter and sugars. Once those are mixed and smooth, add in the buttermilk, vanilla extract and reduced apple cider. Mix thoroughly. Add your mixture of wet ingredients into the large bowl of dry ingredients. Whisk together gently, and be sure to not overmix! This is important to give it a chewy, doughy texture.
Pour your batter into your donut pan, filling each mold ¾ full. If you add more, they will puff up and lose the hole in the middle, and then you will have one sad-looking donut. We don't want that, now do we? Bake for 7-8 minutes until golden.
While the donuts are cooling, mix together your sugar and cinnamon for the coating. Once they have cooled, use a pastry brush to apply a light coat of melted butter to each donut, and then dip them in the cinnamon sugar mixture. Pour yourself a cold glass of milk and bite into these warm, spiced treats and savor every bite!