Preheat oven to 350 degrees. Line one standard size muffin pan with liners or grease with baking spray, set aside.
In the bowl of a stand mixer with mixing speed on low, combine sugars, puree, vegetable oil, applesauce, water, and vanilla extract. Add eggs, one at a time, mixing until just combined.
In a medium size mixing bowl, whisk together flour, salt, baking soda, baking powder, pumpkin pie spice, and ground cinnamon. With mixing speed on low, gradually add in the dry ingredients, mixing until no flour pockets remain. Remove bowl from stand, gently fold in carrot and zucchini, set aside.
Place in oven and bake for 18-22 minutes or until the tops spring back and are golden brown in color. Remove from oven and allow to cool in the pan for 5 minutes before transferring to a wire rack to cool completely.
While muffins cool, to make the whipped topping, combine all ingredients in the bowl of a stand mixer fitted with the whisk attachment. Gradually bring up the mixing speed to high, beat until smooth, about 2-3 minutes. The mixture should be very soft and spreadable, this is like frosting, but with less sugar. If more milk is needed to create a smoother consistency, add more and continue beating. Spread onto the tops of the cooled muffins.