Preheat oven to 375°F (190°C).
Cook brown rice according to package instructions using water or vegetable broth.
Steam or blanch broccoli florets until tender but still crisp.
In a large bowl, mix cooked rice, broccoli, cheddar cheese, Greek yogurt, milk, olive oil, garlic powder, salt, and pepper.
Transfer mixture to a greased baking dish and sprinkle breadcrumbs on top if using.
Bake uncovered for 25–30 minutes until top is golden and casserole is heated through.