Combine all cake ingredients into a large mixing bowl or the bowl of a stand mixer. Mix until well combined into a thick batter.
Note: If your batter seems too dry, you can add a bit of water or dairy-free milk to loosen it up. This is due to the varying moisture levels found in carrots.
Evenly distribute the batter between the three baking pans and bake for 30-35 minutes or until a toothpick inserted in the middle comes out clean.
Allow the cakes to cool for about 10 minutes in the pan. Then turn them out onto a wire rack to cool completely.
While the cakes are cooling, prepare your vegan cream cheese icing by creaming together the vegan cream cheese, vegan margarine, vanilla extract, and maple syrup until smooth. (This is best done in a stand mixer.)
Slowly add in one cup of confectioners sugar at a time, whisking until combined. Continue mixing on high until the frosting is nice and fluffy.
Assemble the cake by placing one layer on a cake stand or plate and topping with about ½ cup of the frosting and leveling with a spatula. Continue with all layers.
Finally cover the entire cake with the frosting, and top with chopped walnuts or pecans, if desired. Enjoy!
To make ONE flax egg: Whisk together 1 tbsp ground flaxseed and 3 tbsp water.