Preheat oven to 350 degrees F. Spray an 8x8-inch baking dish with nonstick cooking spray; set aside.
In a large mixing bowl, combine protein powder, flour, sweetener, baking soda, salt, ginger and cinnamon.
Add vanilla extract, grated carrots, applesauce, yogurt and egg.
Spread batter in prepared pan and bake for 25-30 minutes, or until set in the center. Remove from oven and let cool.
In a mixing bowl, beat together frosting ingredients until light and fluffy. Spread on top of cooled cake. Cut into slices and serve. Garnish with chopped walnuts, if desired (log separately).