In a Dutch oven, saute the carrot, celery, onion and red pepper in 4 tablespoons butter until vegetables are tender. Stir in the broth, broccoli, potato, Worcestershire and cayenne; bring to a boil. Reduce heat; cover and simmer 10-15 minutes or until broccoli and potato are tender.
Meanwhile in a large saucepan, melt remaining butter over medium heat. Whisk in flour until smooth. Gradually whisk in milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Reduce heat. Add cheese; stir just until cheese is melted.
Slowly stir cheese sauce into vegetable mixture. Garnish with additional cheese if desired.