Preheat the oven to 325 degrees and prepare two donut pans by spraying with nonstick cooking spray.
Pour the apple cider in a small saucepan and heat over medium heat. When the cider begins to simmer, reduce heat to low and cook until reduced by half, to around ½ cup.
While the cider is simmering, combine the flour, sugar, brown sugar, cinnamon, and salt in a large bowl.
Add the milk, eggs, and vanilla and beat to combine.
When the cider is reduced, remove from heat. Add the butter and stir until melted.
Allow the cider mixture to cool slightly, then add it to the flour mixture. Beat until combined.
Pipe the batter into the prepared donut pans and bake for 10 minutes.
Remove from the oven and allow to cool slightly in the pan, then transfer to a wire cooling rack to cool completely.
To prepare the topping, mix together the powdered sugar and cinnamon in a large zip-top bag.
Brush the donuts with the melted butter.
Place one or two donuts in the bag. Close the bag and shake to coat the donuts with sugar.
Your delicious baked apple cider donuts are ready to eat! Enjoy!