Heat apple cider in a small saucepan, covered, over medium heat until reduced to 1/3 cup. It will become a thick syrup. Set aside to cool.
In a large mixing bowl, add egg, sugars, coconut oil, milk, and vanilla extract and mix until smooth.
In another mixing bowl, whisk together flour, baking powder, baking soda, cinnamon, and nutmeg.
Dump the dry mixture into the wet mixture, along with the reduced apple cider, and mix until just combined. Don’t over-mix! Batter will be sticky!
Pour batter in a greased donut pan, filling only halfway. You can do this using a cookie scoop, spoon, or put the batter into a frosting bag with a big round tip (I like this way best.)
Bake at 350 degrees F for about 10 minutes or until an inserted toothpick comes out clean.
Cool for 5 minutes and then remove from pan.
While the donuts are cooling, mix together cinnamon and sugar in a bowl or dish wide enough to easily fit the donuts in flat.
Brush melted butter all over each donut and roll in the bowl of sugar until fully coated. I only buttered and sugared one side, but you can do both if you want! For an extra treat you can also drizzle caramel sauce on the top. I recommend doing this as you are eating them so it doesn't make a mess it whatever container you store them in.
Serve warm or room temp.