Pre heat oven to 350 degrees. Line 2 -8 inch cake pans with parchment round , coat parchment and inside of pans with cooking spray. Set aside.
In a medium bowl, sift the flour with cinnamon, nutmeg, baking soda, baking powder and salt- set aside.
In a stand mixer, beat eggs with sweetener, add in applesauce, yogurt and vanilla. Slowly add flour mixture until well combined. Fold in carrots, pecans, coconut. Let batter rest for 10 minutes. The coconut flour needs time to absorb the wet ingredients. Batter will be very thick.
Divide the batter into equal parts and pour into the prepared cake pans. Bake at 350 for 35-40 minutes or until a cake tester comes out clean. Remove cake from pans and let cool completely on a wire rack before frosting.
For the frosting: Using a stand mixer with a whisk attachment, beat cream cheese & yogurt on high until fluffy and creamy.
Add in vanilla and orange zest. .
With the mixer on low, slowly add in the powdered sweetener. Once combined, increase mixer speed to high and beat 2-3 minutes until frosting is light and fluffy. You can use powdered sugar or icing sugar- it will just add calories.
On a cake pedestal, place one layer of the cake. Place strips of parchment paper under the edges of the base layer of cake. This will protect the cake stand from messy frosting.
Spread approximately 3/4 cup of the frosting on the base layer.
Top with remaining cake layer.
Spread a thin layer of frosting all over the cake to form the crumb coat. Let it set for 3-5 minutes in the fridge. Ice the entire cake with remaining frosting. Remove the parchment strips from underneath the base layer. Chill iced cake at least 1 hour or overnight in the fridge. Garnish with carrot peels, or pecans halves.