"I was looking for ways to use up the carrot pulp from my juicer and came across a good recipe for whole wheat carrot cake. I decided to make some substantial changes that resulted in a cake that is flavorful and very light. The juicer makes the carrot pulp so fine that it does not weigh down the cake. I'm sure the recipe will work with grated carrots, too, but I have not tried it."
Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch cake pan.
Whisk honey, grapeseed oil, eggs, and egg whites together in a bowl.
Mix whole wheat flour, cinnamon, baking soda, baking powder, salt, nutmeg, ginger, and allspice together in a large bowl. Make a well in the center; pour in honey mixture. Mix gently until batter is just combined.
Fold carrot pulp, apple, and walnuts into the batter. Pour batter into the prepared cake pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 35 to 40 minutes. Set pan on a wire rack and let cake cool completely, about 30 minutes.
Combine Neufchatel cheese, confectioners' sugar, vanilla extract, and lemon zest in a bowl; beat with an electric mixer until frosting is smooth. Spread frosting over cooled cake.