Preheat oven to 350 degrees F
In a small saucepan, bring the apple cider to a mild boil. Cover and let simmer until the apple cider has reduced to 1/2 cup (about 10 minute). Let cool for 5-10 min.
In a mixing bowl, combine butter and sugar. Add in applesauce, milk, apple cider, and vanilla extract and mix until smooth. Finally, mix in flour, cinnamon and baking powder.
Fill 6 large donut slots (greased) to the top. Bake for 12-14 minutes.
Let cool completely. Dip each donut in butter, then in cinnamon sugar mixture & enjoy!