To make the Apple Cider Syrup: In a small heavy bottomed saucepan heat apple cider with 1/2 cup sugar. Bring to a boil, then lower to medium-low, letting it simmer and reduce until it's around 1/3 cup syrup. (This could take as long as 15-20 minutes.) Remove from heat and cool completely.
To make Doughnuts: Preheat the oven to 350°F. Spray two 6 cup doughnut pans with cooking spray or baking spray.
To a large bowl add flour, baking powder, apple pie spice, baking soda and salt. Use a whisk to sift together.
In a separate bowl, whisk together cooled apple cider syrup, buttermilk, butter, vanilla, granulated sugar, brown sugar and egg.
Add the wet to the dry ingredients, mixing by hand until fully combined.
Use a Tablespoon or a Ziploc bag with the corner snipped off to divide the batter between the wells filling 1/2 full.
Bake for 18-20 minutes or until a toothpick inserted into the center of the batter comes back clean. Allow the doughnuts to cool in the pan for 5 minutes then transfer to a cooling rack while you make the coating.
To make the Cinnamon Sugar Coating: Melt 6 Tablespoon of butter in the microwave. In a separate shallow bowl, toss together the sugar and cinnamon,
Brush doughnuts on all sides with butter then roll in cinnamon sugar. Place back onto the cooling rack to cool completely.
Store Apple Cider Doughnuts in an airtight container at room temperature for up to 3 days.