Melt 2 tablespoons of butter in a medium stockpot before sauteing the celery and garlic until tender. Simmer the broccoli and broth while covered for fifteen minutes.
In the interim, melt 3 tablespoons of butter in a small saucepan over low heat; stir in flour and milk. Stir until the mixture becomes viscous and carbonated.
Blend the soup in segments by pulsing it for a few seconds before pureeing it until smooth.
To the flour mixture, add broth. After seasoning with pepper and garlic salt, incorporate the cheddar cheese.
Garnish with additional cheese and bacon, if desired.