Prepare the Muffin Pan. Preheat the oven to 350°F. Line a 12-cup muffin pan with cupcake liners. Grate the Carrots. Peel and chop whole carrots into 3″ pieces, then weigh out approximately 220g. (You’ll want that extra 20g to account for what gets stuck in the shredder!) Using a KitchenAid attachment, food processor, or box grater, shred the carrots quickly.
Finely Chop the Carrots. Once shredded, give them a final rough chop so the finer pieces distribute evenly throughout the batter. Weigh one last time to ensure you have exactly 200g of moist, fresh carrots.
Whisk the Dry Ingredients. In a medium-sized bowl, whisk together the gluten-free flour, almond flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves. Set this aside.
Beat the Eggs and Sugars. In a large bowl or stand mixer fitted with the whisk attachment, beat the eggs, cane sugar, and dark brown sugar on medium-high speed for 4–5 minutes. You are looking for the mixture to double in volume and become light and fluffy—this aeration is the secret to a light, tender crumb! Once achieved, slowly pour in the melted coconut oil, applesauce, and vanilla extract, mixing for another 1–2 minutes until fully combined.
Combine and Fold. Add the dry ingredients to the wet mixture, mixing until just combined; it's okay to still see a few floury streaks. Turn off the mixer and use a spatula to gently fold in the shredded carrots (and any optional mix-ins) until they are evenly distributed.
Portion and Bake. Using a large cookie scoop, divide the batter evenly among the liners, filling them about ¾ full to prevent the batter from spilling over as they rise. Bake for 18–22 minutes—ours are usually perfect at the 20-minute mark—or until a toothpick inserted into the center comes out clean.
Cool Completely. Transfer the cupcakes to a wire rack and allow them to cool completely. This is a crucial step to ensure your frosting stays perfectly whipped and doesn't melt!