In a Dutch oven, melt butter over medium heat. Stir in flour. Add onion and carrot; cook for 5 minutes, stirring constantly. Gradually add chicken stock and cream, stirring until smooth. Bring to a simmer. Reduce heat to medium-low; cook for 15 to 20 minutes, or until thickened. Add broccoli; cook for 15 to 20 minutes, or until tender. Reduce heat to low; add cheeses, black pepper, salt, and red pepper, stirring until cheese melts.