Coat 2 regular-sized donut pans with cooking spray. (Regular-sized donut pans typically have 6 cavities.)
In a large bowl, combine flour, sugars, baking powder, salt, cinnamon, and cardamom.
In another bowl, whisk together egg, buttermilk, and carrots.
Mix the wet ingredients into the dry ingredients until just combined.
Pour batter into a gallon-sized ziploc bag, and snip off the corner of the bag.
Pipe the batter into the baking pans, filling each donut cup about 3/4 full.
Bake at 350 degrees for 15-17 minutes, or until a toothpick comes out clean.
Allow to cool for 5 minutes, then flip the pans over and tap the donuts out onto a wire rack. Cool completely.