Heat olive oil and crushed garlic in a large skillet. Stir in smoked sausage slices and cook until browned on all sides.
Add pepper, onion, broccoli, chicken broth, and tomato sauce. Simmer until vegetables are tender and the liquid is absorbed, about 10 minutes.
In the meantime, cook rice according to package instructions.
Stir cooked rice into the skillet, sprinkle with cheese, and serve.