Preheat oven to 350°F. Grease a 9x1½-inch round baking pan (or line with parchment paper and grease the paper); set aside. In a small bowl, combine flour, cinnamon, baking soda and nutmeg; set aside.
In a medium bowl, stir together applesauce, granulated sugar, brown sugar, egg and oil. Stir in shredded carrots. Add flour mixture, stirring just until combined.
Spread batter in the prepared pan. Bake for 20 to 25 minutes or until a toothpick inserted near the center comes out clean. Cool in pan on a wire rack for 10 minutes. Remove from pan. Peel off parchment paper, if using. Cool completely on wire rack. Coarsely crumble cooled cake (the crumbles will be dense and moist).
In a medium bowl, fold together dessert topping, baby food carrots and ginger just until combined.
Divide half of the crumbled cake among ten 6-ounce parfait glasses or dessert dishes. Top with half of the dessert topping mixture. Top with pineapple. Top with the remaining crumbled cake and the remaining dessert topping mixture. Sprinkle with walnuts.
Tip: If using sugar substitutes, choose Splenda® Sugar Blend for Baking to substitute for the granulated sugar and Splenda® Brown Sugar Blend to substitute for the brown sugar. Follow package directions to use product amounts equivalent to ¼ cup of each sugar. Nutrition per serving with substitute: same as below, except 182 calories, 100 mg sodium, 28 g carbohydrate, 9 g sugar. Exchanges: 0 other carbohydrate, 0 vegetable, 1 fruit.