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 thickened and cheese is melted, stirring frequently. Stir in broccoli and reserved cooking liquid.