Preheat the oven to 350 ° Lightly grease three 6-cup donut pans.
Add the apple cider to a saucepan and bring to a boil. Reduce heat to low and simmer until cider is ⅓ cup in volume, about 20 minutes. Let cool.
Whisk together the all-purpose flour, baking powder, baking soda, cinnamon and salt.
In a separate bowl, mix the egg, sugars, melted butter, milk and vanilla.
Add the dry ingredients into the wet ingredients and mix until just moistened; do not over mix.
Fill the donut pans so each mold is ¾ full. Note: Use a piping bag for easy fill.
Bake the donuts for about 15 minutes or until a wooden toothpick inserted into the center comes out clean. Invert the donut pan onto a cooling rack.
To make the topping, whisk the sugar and cinnamon together. Brush the tops and sides of the donuts with the melted butter and dip into the cinnamon sugar.