Preheat the oven to 400°F.
Cook the rice according to the directions on the package. Once cooked, drain any excess water if needed and season with salt and pepper.
Add the butter and oil to a saucepan over medium heat. Sauté the onions and garlic until softened, about 5 minutes. Stir in the flour and cook for 2 minutes. Stir in the milk, broth, and cheese.
Add the broccoli and cover with a lid. Simmer for 6-8 minutes until the broccoli is tender.
Place the sausage on a foil-lined baking sheet and cook in the oven until nicely browned, turning over half way through, to an internal temperature of 155°F using a thermometer, about 15 minutes. Then set aside to rest for 3 minutes before slicing.
Mix the rice with the broccoli. Season with salt and pepper to taste.
Top with sliced sausage and serve with bread.