Chop broccoli, onion, pepper and parsley very fine. In saucepan melt butter and saute the chopped vegetable mixture for a few minutes. Add chicken stock and bay leaf. Bring to a boil, cover and let simmer for 30 minutes. Remove and discard bay leaf.
Puree mixture until smooth in blender or food processor. Return soup to low heat.
Combine cornstarch and cold water and stir mixture into soup.