Preheat your oven to 350°F (175°C). Grease a 9x13 inch baking dish.
In a large mixing bowl, combine the cooked rice, cheddar cheese, mozzarella cheese, milk, sour cream, Parmesan cheese, garlic powder, onion powder, salt, and black pepper. Mix until well combined. If using, fold in the peas and diced ham or chicken.
Pour the rice mixture into the prepared baking dish, spreading it evenly.
In a small bowl, melt the butter and mix it with the breadcrumbs. Sprinkle the breadcrumb mixture evenly over the top of the casserole.
Bake in the preheated oven for 25-30 minutes, or until the cheese is bubbly and the top is golden brown.
Remove from the oven and let it cool for 5 minutes before serving.