Combine chicken broth, water, half & half, cheese, flour, onion and pepper in a large saucepan. Whisk to combine and to break up any lumps of flour, then turn heat to medium/high.
Bring soup to a boil, then reduce heat to low. Add broccoli to soup and simmer for 15-20 minutes or until broccoli is tender but not soft.
For each serving spoon one cup of soup into a bowl and garnish with a tablespoon of shredded cheese and a pinch of parsley.
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