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 flours, cinnamon, baking soda and powder, salt and nutmeg.
In a separate, large bowl, using an electric hand mixer, beat the eggs, oil, sweetener 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. Your batter will be very 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.
To make the frosting:
In a large bowl, using an electric hand mixer, beat together the cream cheese and butter 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.
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.
*like all gluten free baking, please weigh your flour to ensure results as different brands have different weights. **You can PROBABLY use whatever sugar free sweetener you prefer. However, only Swerve has been tested with this recipe. You could also use regular sugar, but will obviously change the nutritional information.***Make sure you cut the pecans very small or it makes it hard to cut the cake as they make it break in areas.Total time includes does not include chilling the crumb coat or letting the baked cake cool.