Preheat oven to 325 degrees F. Line bottom of three (6-inch) round, OR two (8-inch round), or one 9-inch round baking pans with parchment paper.
Add roughly chopped carrots to food processor and pulse until very finely chopped. Add pecans and pulse until well combined. Set aside.
Add light brown sugar, superfine sugar, all-purpose flour, baking powder, baking soda, and ground cinnamon to large mixing bowl. Whisk to combine.
Add carrot mixture to flour mixture and stir to combine.
Add vegetable oil, Greek yogurt, egg and vanilla bean paste to small bowl. Whisk to combine.
Add egg mixture to flour mixture. Fold together with spatula until smooth.
Divide cake batter evenly between cake pans. Bake 45 to 60 minutes (depending on the size of pan you’ve chosen), or until cakes are set, and a toothpick inserted in the center comes out dry.
Remove pans from oven and place on wire rack. Allow cakes to cool completely before inverting and removing from pans.
Remove parchment from bottoms of cake layers.