Add apple cider into a saucepan and heat over medium flame. Bring it to a boil and then simmer, stirring occasionally, until it reduces to about 1/2 cup. Depending on the temperature it could take from 20 - 25 minutes. keep it aside until it cools down.
Preheat the oven to 375°F (190°C) (190 degrees C). Grease two 6-cup doughnut pans with butter or non-stick spray. Set aside.
Whisk all dry ingredients. In a large mixing bowl, combine flour, baking soda, baking powder, salt, 1 teaspoon cinnamon, cardamom, and nutmeg. Keep away until needed.
In a separate bowl, whisk together 2 tablespoons of melted butter, 1/2 cup white sugar, 1/2 cup brown sugar, milk, egg, and vanilla extract until well combined. Pour the reduced apple cider and then add dry ingredients. Whisk together to make a little thick batter. Do not overmix the ingredients.
To make it easier, use a large Ziploc bag to pipe the batter into the prepared doughnut pans, filling them about ¾ th. Add the batter into a large Ziploc bag and cut a corner off the bottom of the bag and pipe the batter halfway into each doughnut cup.
Bake in the preheated oven for 10 to 12 minutes, or until the tops are lightly browned and the donuts bounce back slightly when touched. Allow cooling in the pans for 10 minutes before transferring to a cooling rack.
Optional: In a shallow dish, combine the granulated sugar and cinnamon. While the donut is still warm, brush or dip both sides of each donut in the melted butter, then toss in donuts to coat lightly.