Preheat your oven to 350 degrees and line two 8 inch cake pans with parchment paper, spraying the exposed sides with cooking spray. Set aside.
In a medium bowl, stir together the coconut flour, cinnamon, baking soda and powder, salt and nutmeg.
In a separate, large bowl, using an electric hand mixer, beat the eggs, sweetener, Greek yogurt and vanilla until well combined. Stir in the coconut flour mixture and stir until combined.
Gently fold in the carrots, pecans and coconut flakes until well combined. Let the batter stand for 10 minutes so the coconut flour can begin to absorb the moisture. Your batter will be thick, this is normal.
Divide the batter evenly between the 2 pans, spreading out smoothly. Bake until the sides are golden brown and a toothpick inserted in the center comes out clean, about 35-40 minutes. Let cool COMPLETELY before frosting.