Preheat your oven to 350°F (175°C).
Prepare the broccoli by steaming it until tender, about 5 minutes.
In a skillet, heat olive oil over medium heat and sauté the diced onion and minced garlic until softened, about 5 minutes.
In a large mixing bowl, combine sour cream, mayonnaise, cooked rice, salt, and pepper.
Fold in the steamed broccoli, sautéed onion and garlic, and 1.5 cups of cheddar cheese into the mixture.
Transfer the mixture to a greased casserole dish and smooth the top.
Sprinkle the remaining cheddar cheese and crushed crackers or breadcrumbs evenly on top.
Bake in the preheated oven for 25-30 minutes, or until bubbly and golden on top.
Let the casserole cool for a few minutes before serving.