Preheat your oven to 350°F (175°C).
In a medium saucepan, heat olive oil over medium heat. Add the sliced carrots and bell peppers, and sauté for about 3-4 minutes until they begin to soften.
In a large mixing bowl, combine the broccoli, cauliflower, corn, sautéed carrots, and bell peppers.
In a separate bowl, whisk together the heavy cream, garlic powder, onion powder, salt, and pepper. Pour this mixture over the vegetables and stir until well combined.
Add the shredded cheddar cheese and mozzarella cheese to the vegetable mixture and mix.
Transfer the vegetable mixture into the greased 9x13 inch baking dish.
Sprinkle the breadcrumbs evenly on top of the casserole.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and the cheese is bubbly.
Remove from the oven and let it cool for a few minutes before serving. Garnish with fresh parsley if desired.