In a large saucepan, mix chicken broth, onion, broccoli, garlic powder, thyme, and bay leaves. Bring to a boil. Reduce heat, cover, and simmer 10 minutes, or until vegetables are soft.
Remove bay leaves and pour mixture into a food processor.
Pulse until smooth, approximately 1 minute.
In the original saucepan, melt butter. Whisk in flour, salt and a little pepper until a thick paste forms. Add milk and cook, stirring constantly until mixture thickens. Add cheddar, red pepper and Worcestershire sauce; stir until cheese dissolves.
Pour in broccoli mixture and cook until blended. If necessary, add more chicken broth to thin. Season with additional salt and pepper as needed.
Serve over additional steamed broccoli pieces. (optional)