In a medium saucepan over medium-high heat, saute onion and carrot in margarine or butter until onions begin to brown. Add broth and broccoli. Simmer until broccoli is tender, 5 to 7 minutes.
In another container, slowly stir the milk into the flour until smooth. Stir the milk mixture into the soup. Bring to a boil and continue stirring until slightly thickened, 3-5 minutes
Add cheese and pepper. Heat over low heat until cheese is melted. Serve hot.
Refrigerate leftovers within 2 hours.