Cook broccoli in chicken broth until broccoli is tender. In another pan, sauté onion in the butter. Add flour and cook on low for 5 minutes. Add this mixture to the broccoli and chicken broth and bring to a boil. Simmer for 10 minutes. Add cheddar cheese and let melt. Add milk and sour cream; simmer for an additional 10 minutes. This is good served with warm French bread.