In large saucepan, cook onion in butter until tender. Stir in flour, salt and pepper. Add milk all at once. Cook until thickened, stirring constantly, about 1 minute. Add cheese and stir until melted. Remove from heat.
Heat water in medium saucepan. Add bouillon cubes and bay leaf to water. Bring to boil. Add broccoli and cook as package directs: do not drain.
Add broccoli and cooking liquid to cheese mixture. Blend well. Remove bay leaf.