Pour the apple cider into a small saucepan. Bring to a boil over medium heat, and then lower the heat to a rolling simmer. Let the cider simmer, stirring occasionally, until it reduces to a 1/2 cup. This should take between 40-50 minutes. Remove from heat, pour into a heat-proof bowl, and let cool until it's lukewarm.

Preheat the oven to 375°F. Grease a donut pan** with baking spray or neutral oil. Set aside.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, apple pie spice, and cardamom. In a separate medium bowl, whisk together the melted butter, brown sugar, white sugar, egg, and vanilla extract until smooth. Stir in the boiled cider until incorporated.

Add half of the dry mixture to the wet mixture, followed by half of the milk. Repeat with the remaining ingredients, stirring just until mixed. The batter will be fairly thick. Using a piping bag, pipe the batter into the molds until it comes up about halfway.

Bake the donuts for about 8-9 minutes, just until an inserted toothpick comes out clean. Let the donuts cool for about 5 minutes in a pan before transferring them to a cooling rack.

In a small, shallow bowl, stir together the sugar, cinnamon, and cardamom until combined.

Brush the bottom of each donut with melted butter, and dip the donuts into the cardamom sugar. Repeat with the tops of the donuts. Serve immediately and enjoy!