In a large stock pot or dutch oven, cook onion in butter until tender. 5-7 minutes.
Once onion is cooked, add garlic in to cook for 30 seconds.
Stir in flour & pepper. Whisk for 1-2 minutes, until flour is cooked.
Slowly add milk while whisking. Whisk until slightly thickened, stirring constantly.
Add cheese & stir until melted. Once melted remove from heat. (do not boil)
In a separate small saucepan, combine water, bouillon paste and broccoli.
Cook broccoli until pieces are soft and tender. DO NOT DRAIN.
Combine the cooked broccoli & water with the cheese soup.
Stir together until well combined. Heat until hot, do not boil.
Serve with crusty bread.