Preheat the oven to 350 F. Spray a round bundt baking pan with non-fat cooking spray.
Combine the flour, sugar (substitute), 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 shredded carrots, applesauce, oil, nuts, 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 minutes.
Let completely cool and using a knife gently seperate any sticking edges from the pan.
While waiting to cool, start your frosting.
Beat/Cream together cream cheese, powdered sugar and vanilla until smooth.
*Add milk if you want a thinner glaze.
When the cake is cooled, have your serving plate ready. Place the plate over the top of the bundt pan (area open to the cake) and flip the bundt pan and plate (holding tightly together) right side up so that the cake will easily stand on the plate when the pan is lifted up and off.
Frost by either drizzing frosting over the cake or give a good thick layer.
(I cut mine in half and did half with frosting and half without)