Pour 2 cups of apple cider into a small saucepan and bring to a simmer over medium heat. Let it reduce until you have ½ cup of concentrated cider, about 15-20 minutes. Allow the reduced cider to cool completely before using.
Preheat your oven to 350°F (175°C). Grease two 6-cavity donut pans with non-stick spray or butter.
In a large bowl, whisk together the flour, baking soda, baking powder, cinnamon, nutmeg, cloves, optional cardamom, and salt.
In a separate bowl, whisk the eggs, brown sugar, and granulated sugar vigorously until light and fluffy, about 90 seconds. Add the melted butter, buttermilk, cooled cider reduction, and vanilla extract. Mix until well combined.
Pour the wet ingredients into the dry ingredients and fold together gently with a spatula until just combined. Stop mixing when no dry flour pockets remain but the batter still looks slightly lumpy.
Spoon the batter into the prepared donut pans, filling each cavity about ¾ full. For the cleanest transfer, use a piping bag or a zip-top bag with the corner snipped off.
Bake in the preheated oven for 12-14 minutes, or until the donuts spring back when lightly touched and a toothpick inserted comes out clean.
While the donuts are baking, mix the granulated sugar and cinnamon in a shallow bowl for the coating. Melt the butter in another small bowl if using the butter method for coating.
Allow the donuts to cool in the pan for 5 minutes, then carefully remove them. While still warm (but not hot), brush each donut lightly with melted butter and then roll in the cinnamon-sugar mixture.