In a large saucepan, cook sausage and onion in oil until lightly browned; drain. Stir in the carrots, potatoes with contents of sauce mix, water and pepper. Bring to a boil. Reduce heat; cover and simmer for 10-20 minutes or until vegetables are tender.
Stir in broccoli; cover and cook 5 minutes longer or until heated through.
Sprinkle with cheese; cover and let stand until cheese is melted.