Preheat oven to 350°F (177°C). Spray donut pan with non-stick spray. Set aside.

Reduce the apple cider.

To reduce your apple cider:
Pour 1½ cups apple cider into a small saucepan.
Place on low heat and set a timer for 10 minutes, stirring occasionally.
Begin checking at 10 minutes, and stir regularly for the next 10 minutes. At this point, apple cider should have reduced to ½ cup. If not, continue to reduce on low heat and stir consistently.
Remove from heat and allow to cool and thicken for at least 20 minutes before using in the batter.

Brown your butter and let it cool

Combine your butter, egg and buttermilk

Combine the dry ingredients together.
all-purpose flour
baking soda
baking powder
ground cinnamon
salt
packed light brown sugar
granulated sugar

Combine the wet ingredients, except the reduced apple cider together.
unsalted butter, melted, browned
1 large egg
buttermilk, at room temperature
pure vanilla extract

Combine the dry and wet ingredients together. At this point, you can add the apple cider. Whisk everything together until smooth and combined. You’ll notice the batter will be slightly thick. We want thick batter for cakey and dense donuts.

Fill the donut pan. Fill each donut cup about halfway.

Bake. for twelve minutes. To test doneness, poke your finger into the top of the donut. If the donut bounces back, they’re done. If not, pop them back in the oven and check on them like you would a newborn baby. Obsessively. ;)

Once they are out of the oven, let them cool for a few minutes, then invert the pan to release the donuts. If you don't let cake donuts cool long enough, they will break and fall apart, so remove them slowly and carefully. 

Melt butter and make your cinnamon sugar coating while you bake.

To make the sugar coating, combine the granulated sugar and cinnamon together in a medium bowl. Brush your warm melted butter on both sides of the donut. Once cool enough to handle, dunk both sides of each donut in the cinnamon sugar topping.