Steam the veggies until crisp-tender, drain well and season with salt and pepper.
Put the vegetables in a greased 8x8 baking pan. Chop up larger vegetable pieces as needed.
In a medium bowl, mix the mayo and the next 3 ingredients- light mayonnaise, cream of mushroom and cheddar cheese. Spoon this mixture over the veggies, tossing as needed to spread mixture as evenly as possible.
Sprinkle the 3 tbsp of Parmesan cheese over the top. Bake at 350 degrees for 20-25 minutes or until the topping is golden and bubbly.