Measure 3 cups of dry instant rice and cook it according to the package instructions, then set aside. Please note that yields for other types of rice are different than instant.
Combine the onion, garlic, carrots, olive oil, salt, and pepper in a large skillet or dutch oven.
Sautee the carrots and onions for 10-15 minutes on medium high heat, until the carrots start to soften and the onions become translucent.
Add the peas, broccoli, cream of mushroom soup, 1 1/2 cups parmesan cheese, and 1 cup of sharp cheddar cheese to the skillet.
Stir the mixture over medium heat until heated through, about 10-12 minutes.
Add the cooked rice and parsley to the skillet and stir to combine.
Transfer the veggie casserole mixture to a greased large 9 x 13 casserole dish.
Top the casserole with the remaining 1 cup of parmesan cheese and 1 cup of sharp cheddar cheese.
Bake the vegetable rice casserole at 400 degrees for 10-15 minutes , until the cheese is bubbly and beginning to brown