Pour 1 ½ cups of apple cider in a sauce pan and bring it to boil. Then reduce the heat to medium/low and simmer the liquid for about 20 minutes until you get ½ cup of reduced liquid.
When done, let it cool off before adding it to the batter.
In a medium size mixing bowl, whisk together melted butter, brown and granulated sugar, an egg, vanilla extract, buttermilk and reduced and chilled apple cider.
In another mixing bowl, mix flour, baking soda, baking powder, ground cinnamon, apple pie spice, and salt.
Add dry ingredients to the wet ingredients and mix until smooth consistency.
Transfer the mixture to a piping bag, snip the tip of the bag and pipe the mixture into the greased donut pan. Fill it only about halfway.
Bake donuts for 10 minutes at 350°F.
When done, take them out of the oven, let them sit in the donut pan for 3-5 minutes, then transfer to a wire rack.
To coat, dip the donuts in melted butter or brush with baking brush from both sides.
In a smaller mixing bowl, mix together granulated sugar, ground cinnamon, and apple pie spice and dip the buttered donuts into the mixture. Make sure they are covered from all the sides.
Let them dry on the wire rack, then transfer to an air tight container.