In a soup pot, bring water and chicken broth to a boil. Add broccoli and onion and boil 10 minutes. Add seasonings and shredded cheese and stir until melted. Add milk, cream and butter. Stir until fully mixed. Using a hand blender, purée soup. Bring to boiling. Slowly add water to flour, stirring constantly until texture is smooth. Slowly add water, stirring rapidly. Cook until soup is consistency of heavy cream.