Preheat the oven to 350°. Grease a donuts pan. If you do not have a donuts pan, you can also use a muffin tin.
In a small sauce-pan, reduce the apple cider. This should take about 20-30 minutes. Let the cider come to a boil and then reduce to a simmer. A lot of the liquid will reduce. Let the cider reduce until there is about ½ cup left. Take off the heat and let cool.
In a medium-sized bowl, combine the dry ingredients. Mix together the flour, baking soda, baking powder, spices, and salt. Set aside.
In a large bowl, mix together the wet ingredients with a whisk. Mix together the eggs, apple sauce, sugars, vanilla, and oil until smooth.
Slowly add in the flour mixture to the egg mixture using a whisk. Mix until combined.
Once the mixture is combined, add in the apple cider. Make sure the cider is fully mixed in. You want the mixture to be on the thicker side and not too loose.
Add the mixture to the donuts pan. In order to do this without making a mess, I transferred the batter to a measuring cup for an easy pour. Fill the donuts about ¾th of the way full.
Bake the donuts for about 14-18 minutes. They will start to pull away from the sides when they are done. Let cool for about 5-7 minutes before removing from the pan. Repeat with the remaining batter.
While the donuts are still warm, mix them in the cinnamon sugar mixture. Mix the cinnamon and sugar in a small bowl and gently toss until covered.
The donuts will taste best eaten immediately They will last a few days in an air-tight container, but will be a little stale.
