In a large saucepan, bring water and bouillon to a boil.
Add broccoli.
Reduce heat; cover and simmer for 3-4 minutes or until crisp-tender.
Drain, reserving 3/4 cup liquid.
In another large saucepan, saute onion in butter until tender.
Whisk in flour until blended.
Add the milk and cheese.
Cook over medium-low heat until cheese is melted, stirring frequently.
Stir in broccoli and reserved cooking liquid.
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