Preheat the oven to 375°F (for high-altitude) or 350°F (for sea-level). Grease a donut pan or cupcake tin. In a small bowl, combine the flour, baking powder, baking soda, cardamom, cinnamon, nutmeg, and salt. Set aside.
In a medium bowl, whisk together the brown sugar, sugar, buttermilk, canola oil, vanilla, and egg until smooth. Add the shredded carrots and chopped nuts until combined. Then, stir the flour mixture into the wet ingredients until just combined.
Spoon the batter into a large piping bag (or a plastic bag with the tip cut off). Pipe the batter into the donut pan cavities about 1/2 way full (don’t go more than halfway, or the batter will rise too much and you won’t get a hole in the center). Bake for about 8-9 minutes, until a toothpick comes out clean.
Let the donuts cool in the pan for about 10 minutes, and then let them cool completely on a rack.