Preheat the oven 375˚F. Lightly spray two donut pans with cooking spray and set aside.
Heat the apple cider in a small saucepan over medium heat. Bring to a simmer and allow to cook until the cider is reduced to around a 1/2 cup. Remove from heat.
In a large bowl, mix together the flour, baking powder, baking soda, salt, cinnamon, all-spice, and nutmeg. Set aside.
In a separate bowl, cream together the sugars, milk, 2 Tablespoons butter, vanilla, and egg.
Slowly mix the dry ingredients into the wet ingredients until just combined.
Scoop the batter into a piping bag, or a large ziplock bag with the corner cut out. Pipe the batter into the prepared donut pans, and bake in the preheated oven for 10-12 minutes.
Allow to cool in the pans for around 10 minutes before transfering the donuts to wire racks.
Brush the slightly warm donuts with the remaining butter.
Place the cinnamon sugar in a shallow bowl. Dip the donuts in the cinnamon sugar, and turn to coat on all sides. Return to the wire racks.