In large saucepan, mix chicken broth, onion, broccoli, garlic powder, thyme and bay leaves. Bring to a boil. Reduce heat, cover & simmer 10 min or until vegetables are soft.
Remove bay leaves and pour mixture into a food processor (Or us an immersion blender) Pulse until smooth, approximately 1 min. reserve in a bowl.
In the original saucepan, melt butter. Whisk in flour, salt & a little pepper until a thick paste forms. Add milk and cook, stirring constantly, until mixture thickens. Add cheddar. Stir until it dissolves.
Pour in broccoli mixture & cook until blended. If necessary, add more chicken broth to thin. Season with additional salt & pepper. Serve with bread for dipping.