To make the donuts: In a small saucepan, simmer the apple cider, stirring occasionally, until you’re left with about ½ cup, about 20 minutes. Set aside to cool for 10 minutes.
Heat oven to 350 F. Spray donut pan with non-stick spray.
In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, apple pie spice and salt.
In a small bowl, whisk together the melted butter, egg, brown sugar, granulated sugar, milk and vanilla extract.
Pour the butter mixture into the dry ingredients, add the reduced apple cider and whisk everything together until smooth and combined. Batter will be slightly thick.
Pipe the batter into the donut cups, filling them just under halfway.
Bake for 10 minutes or until the edges and tops are lightly browned. To test, poke your finger into the top of a donut. If the donut bounces back, they’re done.
Cool donuts for 2 minutes then transfer to a wire rack. Regrease the pan and bake the remaining donut batter.
To finish the donuts: Combine the granulated sugar, cinnamon and apple pie spice together in a medium bowl.
Once cool enough to handle, dunk one side of each donut in the melted butter, then coat generously in the apple spice topping — and serve immediately. Leftovers will keep for two days covered tightly at room temperature.