Preheat your oven to 350°F 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.
Divide batter evenly between pans and spread out with a spatula to smooth the tops. Bake for 22-32 minutes in the two 8-inch pans and 30-40 minutes for three 6-inch pans.
Cakes are done when a tester comes out clean or with just a few crumbs attached. Allow cake to cool completely before frosting or removing from the pans. The cake should be room temperature when you frost it. This is very important. Cakes can be made a day ahead if you’d like.
Make your frosting: In a large bowl, using an electric hand mixer, beat together the cream cheese and yogurt on high speed until fluffy. Add in the vanilla and beat until combined.
Set the mixer on low speed and gradually add in the powdered sweetener, until you've added all of it and it's well combined. Return to high speed and beat for 2-3 minutes until the frosting is fluffy.
To frost: Place one layer bottom side up on a cake stand. Spread 3/4 cup of the frosting all over it evenly. Then, place the other cake bottom side up gently on top.
Spread a thin layer of frosting all over the cake to make the crumb coat. It doesn’t have to be pretty, it’s just to seal in the crumbs. Chill for at least an hour, up to overnight. Put the remaining frosting in the fridge too, so it starts to firm up.
Once chilled, frost the entire cake. I find an offset spatula really helps! Garnish with extra pecans, if desired.