Preheat the oven to 350 F. Spray a 13×9 baking pan with non-fat cooking spray.
Combine the flour, sugar, brown sugar, cinnamon, nutmeg, baking soda, and salt in a medium bowl.
Whisk the egg substitute and egg whites in a large bowl. Add the carrots, applesauce, oil, raisins, and water stirring until blended.
Using a sturdy rubber spatula, add the flour mixture to the carrot mixture, and stir until blended. Spread the batter evenly in the pan. Bake until the cake is nicely browned and the edges begin to pull away from the sides of the pan, approx 35-37 minutes.
Place pan on wire rack and cool completely before frosting.
For the Frosting
While the cake is baking, beat the cream cheese and butter together until smooth. Reduce speed to low and beat in the powdered sugar and vanilla. Increase speed to medium-high and beat until smooth. Transfer to a bowl, cover with plastic wrap and store in the refrigerator until ready to use.
When ready to frost the cake, remove the icing from the refrigerator and stir. Spread over top of cake. Cut cake into 16 equal pieces.
Notes
The nutritional information is for 1 piece of frosted cake.