Preheat your oven to 350°F (175°C) and line a 9-inch round cake pan with parchment paper.

In a large bowl, mix together the almond flour, coconut flour, shredded coconut, baking powder, cinnamon, nutmeg, and salt.

In a separate bowl, beat the eggs, coconut oil, applesauce, erythritol, and vanilla extract together until well combined.

Add the wet ingredients to the dry ingredients and stir until just combined.

Fold in the shredded carrots and chopped walnuts, if using.

Pour the batter into the prepared cake pan and smooth out the top with a spatula.

Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.

Let the cake cool completely in the pan before removing it and transferring it to a serving plate.

To make the frosting, beat the cream cheese and butter together in a large bowl until smooth and creamy.

Add the vanilla extract and powdered erythritol and continue to beat until well combined.

Spread the frosting over the top of the cake and serve.

Enjoy your delicious homemade low-carb carrot cake!