In a saucepan, bring the apple cider to a boil. Once boiling, reduce the heat and simmer, stirring occasionally, until the apple cider reduces to ½ cup. This may take about 15 minutes. Remove from the heat and let cool.
Preheat the oven to 350°. Grease a donut pan with non-stick cooking spray.
In a large bowl, mix together the flour, baking powder, baking soda, cinnamon, apple pie spice, and salt.
In a separate bowl, whisk together melted butter, egg, light brown sugar, granulated sugar, milk, and vanilla extract until combined.
When the reduced apple cider is cooled, add it to the wet ingredients along with the shredded apples. Whisk to combine. Then, pour this mixture into the dry ingredients. Stir using a rubber spatula just until combined. The batter should be thick but pourable.
Transfer the batter to the pastry bag. If you don't have one, use a ziplock bag with a corner cut off. Fill each donut cup about ¾ full.
Bake in a preheated oven for 10 minutes or until golden brown. Remove from the oven and let cool slightly. Then, transfer to a cooling rack.
In a small bowl, mix together sugar and cinnamon. Dip each donut into melted butter, then, into a cinnamon sugar mixture until fully coated. Serve immediately. Enjoy!