Heat olive oil in a large skillet over medium heat.
This step is optional: Add cooked sausage to the skillet and sauté till they start to brown, about 6 minutes. Transfer sausage to a plate and keep oil in the skillet.
Add onion, bell pepper, carrots, and garlic to the skillet. Cook till the onions and bell peppers start to soften, about 5 minutes.
Mix in the chicken broth, rice, uncooked broccoli florets, salt, and sausage. Turn the heat to high and bring it to a boil. Then reduce heat to low and cover. Cook for 15-17 minutes, or until the rice is done. Stir occasionally to prevent the rice from sticking to the bottom of the skillet.
Once the rice is done cooking, mix in milk, cheddar cheese, and red pepper flakes. Stir until everything is well combined. Serve immediately.