Preheat your oven to 350°F (175°C).
Grease your cake pans and line the bottoms with parchment paper. This ensures that the cake won't stick to the pans and makes for easy removal.
In a mixing bowl, combine the almond flour, whole wheat flour, coconut flour, erythritol (or stevia), ground cinnamon, ground nutmeg, baking powder, baking soda, and a pinch of salt. Whisk these dry ingredients together until they are well combined. These dry ingredients will form the base of your diabetic carrot cake.
In another mixing bowl, whisk together the eggs, unsweetened applesauce, Greek yogurt, olive oil, and vanilla extract. Ensure that the wet ingredients are thoroughly combined and have a smooth texture. The combination of applesauce and Greek yogurt adds moisture to the cake, while olive oil provides a healthy fat source.
Slowly add the dry ingredients to the wet ingredients while stirring continuously. Use a spatula to fold the dry mixture into the wet mixture until you have a smooth, consistent cake batter. Be careful not to overmix, as this can result in a dense cake.
Gently fold in the grated carrots. Carrots not only provide natural sweetness but also contribute vitamins and fiber to the cake. The vibrant orange color of the carrots is a testament to their rich beta-carotene content, a powerful antioxidant.
Divide the batter evenly between the prepared cake pans. Smooth the tops with a spatula to create an even surface. Place the pans in the preheated oven and bake for approximately 25-30 minutes or until a toothpick inserted into the center of the cakes comes out clean.
Remove the cakes from the oven and let them cool in the pans for about 10 minutes. Then, carefully remove the cakes from the pans and transfer them to a wire cooling rack to cool completely. Cooling the cakes is crucial before frosting to prevent the frosting from melting.
While the cakes are cooling, you can prepare the cream cheese frosting. In a mixing bowl, combine the low-fat cream cheese, unsalted butter, powdered erythritol (or stevia), and vanilla extract. Use a hand mixer or a stand mixer to whip the frosting until it becomes smooth and fluffy. This process usually takes about 2-3 minutes.
Once the cakes have cooled completely, it's time to frost them. Place one cake layer on a serving plate and spread a layer of cream cheese frosting on top. Then, carefully place the second cake layer on top of the frosting. Use the remaining frosting to cover the top and sides of the cake.
If you like a bit of crunch and added flavor, consider sprinkling chopped pecans or walnuts on top of the frosted cake. Nuts not only enhance the texture but also provide healthy fats and protein.