Preheat the oven to 350°F. Line a cupcake tin with paper cups.
Grate the carrots, half of the amount with the coarse side and half with the fine side of the grater.
Finely chop the cranberries, putting aside a small amount for sprinkling on top of frosting if desired.
In a large bowl, lightly whisk together the sugars, oil, pumpkin puree, yogurt and eggs.
In another bowl, mix the flours, baking powder, baking soda, salt, cardamom, cinnamon, nutmeg, cloves and ginger. Gently fold the dry ingredients into the egg mixture until just combined.
Lightly stir in grated carrots and cranberries, taking care not to over-mix. Spoon the batter into the cups, leaving a bit of room for expansion in the oven. Bake until a toothpick inserted in the middle comes out clean, about 18-20 minutes.
To make the frosting: mix cream cheese and butter together with an electric mixer in a bowl until completely combined and clump-free. Add pumpkin puree and mix to combine. Gradually add powdered sugar and mix until the texture is completely smooth. If you prefer a thicker frosting, gradually add more powdered sugar until you reach desired texture. Make sure the cupcakes have cooled completely before frosting them. Sprinkle the tops with finely chopped cranberries.