- 3/4 cup honey
 - 2/3 cup grapeseed oil
 - 2 eggs
 - 3 egg whites
 - 2 cups whole wheat flour
 - 1 tablespoon ground cinnamon
 - 1 1/2 teaspoons baking soda
 - 1 teaspoon baking powder
 - 1/4 teaspoon salt
 - 1/4 teaspoon ground nutmeg
 - 1 pinch ground ginger
 - 1 pinch ground allspice
 - 2 cups carrot pulp from juiced carrots
 - 1 cup peeled minced apple
 - 1/2 cup chopped walnuts
 - Cream Cheese Frosting:
 - 1 (8 ounce) package Neufchatel cheese, at room temperature
 - 1 cup confectioners' sugar
 - 1 teaspoon vanilla extract
 - 1/2 teaspoon lemon zest (optional)
 
- Preheat oven to 350 degrees F (175 degrees C). Grease a 9×13-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.