Bring 5 cups chicken broth to boil in large pot. Add broccoli. Reduce heat and simmer until broccoli is just tender, about 5 minutes.
Meanwhile, whisk eggs and remaining 1/2 cup broth in medium bowl to blend well. Bring soup to boil. Very slowly pour egg mixture into soup without stirring (egg mixture will form fluffy clumps); boil 1 minute. Stir gently to blend. Season soup with salt and pepper. Ladle soup into 4 bowls. Sprinkle each with 1 tablespoon Parmesan cheese.
