Heat a large skillet over medium heat. Brown sausage pieces, about 5 minutes. Remove from the pan.
Add olive oil to the pan and sauté onion, mushrooms, and garlic cloves until tender. Mix in salt, pepper, oregano, and thyme. Add rice and toss to combine.
Stir in cream of chicken soup and chicken broth and bring to a boil. Set broccoli on top of the mixture, cover, and reduce to a simmer. Cook undisturbed for 18-20 minutes or until most of the liquid has been absorbed.
Stir well and top with cheddar cheese. Serve immediately.