Beat together the egg whites, unsweetened applesauce, lemon juice, water, and finely-grated carrot. Add the dry ingredients, baking powder and soda last, and beat until combined. Pour into a well-greased 9-inch cake pan and bake at 350 degrees F for about 19 minutes or until a toothpick inserted in the center comes out cleanly and the center is not mushy but still quite moist. Let the cake set in the pan for a few minutes, then take it out of the pan and let it cool on a wire rack. Refrigerate to chill completely before frosting.
To make the frosting, combine all the frosting ingredients and spread onto the chilled cake. Top with a small amount of toasted unsweetened coconut flakes (a low-fat variety works great) for garnish, if desired. Store cake in the refrigerator. The flavors of the cake are best the day of baking, but it will keep for a few days and still be good. Serves 8-10.
Trim Healthy Mamas, if you keep within the serving size, the fat from the cream cheese will be well within THM:E guidelines (5 grams of fat/serving or less).
Recipe by Briana Thomas at https://www.briana-thomas.com/carrot-cake-with-cream-cheese-frosting/