Pour apple cider into a saucepan, and bring to a simmer. Simmer until cider is reduced to ½ cup, stirring occasionally. This usually takes about 20 minutes.
Once cider is reduced, remove from stove and allow to cool.
Preheat the oven to 350ºF. Spray donut baking pans cooking spray.
In a large mixing bowl, combine flour, sugar, baking powder, cinnamon, and salt.
Make a well in the center of the dry ingredients and add the eggs. Whisk the eggs to break them up, but don’t mix them into the batter yet.
Next add in the cider, milk, vanilla, and oil. Stir until just combined. Don't overmix.
Spoon batter into a pastry bag, or zip-top baggie with the corner cut off.
Squeeze batter into greased donut pans, filling each donut about ⅞ full.
Bake full sized donuts for about 10 to 12 minutes, or mini donut for 9-10 minutes.
Remove from oven and cool on a wire rack.
Mix cinnamon and sugar together in bowl.
Dip the tops of donuts in melted butter, then dip in the cinnamon sugar.
Serve and enjoy!