Preheat the oven to 350ºF. Spray 2 (9-inch) round cake pans with non-fat cooking spray (I used butter flavored Pam), line the bottoms with parchment or wax paper, and spray the paper with the nonstick spray.

Combine the flour, both kinds of 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, butter, and raisins, and hot water stirring until blended. With a rubber spatula, add the flour mixture to the carrot mixture, and stir until blended. Spread the batter evenly in the cake pans. Bake until the cakes are nicely browned and the center of each one bounces back when lightly pressed with a fingertip, approx 30-32 minutes. Let cool for 15 minutes. Remove the cakes from the pans, peel off the paper, and cool completely on racks.

To make the frosting, with an electric mixer on medium-high speed, beat the remaining ingredients until smooth.

Place on layer of cake on a cake plate, and using 1/2 cup of frosting, frost evenly out to edges. Place other layer of cake on top, and spread remaining frosting on top and on sides. Slice into 16 servings.