Preheat oven to 350 degrees. Spray/ butter donut pan and set aside.
In a sauce pan, over medium high heat bring apple cider to a boil. Reduce the heat, and simmer until it's reduced to about 1/2 cup, stirring occasionally. It should take about 20-30 minutes. Remove from heat and allow to cool.
In a mixing bowl, combine 1/2 cup of apple cider, melted butter, eggs, brown sugar, granulated sugar, apple sauce and vanilla. Mix until until combined.
To the wet batter add flour, baking powder, baking soda, cinnamon, nutmeg and salt. Mix until just combined. make sure not to over mix the batter. as this will lead to tough dry donuts.
Add batter to a piping bag, and pipe the batter into the prepped donut pan. filling 2/3 of the donut pan. Bake 12 minutes. Remove and let cool for about 2 minutes.
In a small bowl, melt 1/3 cup butter. In another bowl, combine granulated sugar and cinnamon. Dip both sides of donut in melted butter then into the cinnamon sugar mixture until coated. Serve warm and enjoy!