Preheat the oven to 350ºF and line a cupcake tin with paper liners.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, and spices. Toss in the grated carrots until evenly coated. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, combine both sugars, eggs, greek yogurt, and vanilla, and mix on high until thoroughly incorporated, about 2 minutes. With the mixer on low, slowly drizzle in the coconut oil. Pour this mixture into the flour-carrot mixture and use a rubber spatula to gently fold everything together.
Scoop batter into the prepared cupcake tin, filling each cup about 3/4 full. Bake for 18-20 minutes, or until a toothpick inserted in the center of the cupcake comes out with a few crumbs attached. Remove cupcakes from the oven and allow to cool in the cupcake tin for 10 minutes before transferring to a wire rack to cool completely.