Heat olive oil in a large skillet over medium heat. Add onion, garlic, bell pepper, and carrots. Sauté until softened, about 5 minutes.
In a large bowl, combine the sautéed vegetables, broccoli, brown rice, crushed tomatoes, cream of mushroom soup, vegetable broth, oregano, thyme, and black pepper.
Transfer the mixture to a 9x13-inch casserole dish. Top with shredded cheddar cheese.
Bake in a preheated oven at 375°F (190°C) for 30-35 minutes or until bubbly and golden brown.
