In a large pan combine broth, soup, onion,celery, salt and pepper. Bring to a boil. Reduce heat, cover, and simmer for 20 minutes. Add milk and bring to a boil. In a large bowl, mix cornstarch and water until cornstarch is completely dissolved. Gradually add to soup, stirring constantly. Simmer 5 minutes. Add broccoli and cheese, mixing until cheese melts.
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