In a large, heavy saucepan, melt butter. Add flour and cook several minutes, stirring. Remove from heat. Gradually blend in broth. Bring to boil, stirring, and add broccoli, carrots, celery, onion, garlic, thyme, salt and pepper which have been mixed. Cover and simmer 8 minutes until vegetables are tender. Blend cream and egg. Gradually blend in several teaspoons of soup. Return to soup and cook, stirring until thickened, and blend in cheese.
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