Preheat an oven to 350F and spray two 8" cake pans with nonstick spray. Set aside.
Whisk the eggs together before adding the apple sauce, grated carrots, and vanilla extract. Set aside.
Mix the dry ingredients in a large bowl before gradually stirring in the egg mixture. Be sure you don't have any dry patches of flour but don't over mix the batter.
Transfer the batter to the two cake pans. Each pan should have roughly 530 grams in each unless you modified the recipe. Shake each cake pan to evenly distribute the batter and gently smack a flat surface with the bottom of the cake pan to remove any air bubbles.
Bake for 22-25 minutes or until the cakes are cooked through in the center. (If you bake the cake in one large pan, you may need to bake for 30-40 minutes.)
Remove the carrot cakes from the oven and after they've cooled for a few minutes, transfer them to a cooling rack. Set the cream cheese out to warm to room temp.
Once the cakes have fully cooled, mix the cream cheese and powdered sugar substitute together. Frost the first cake before placing the second cake on top and frosting the top and sides. Gently pat the sides of the cake with walnuts in your hands to coat the sides.