Place butter and flour in a small pan or skillet.
Place over medium high heat.
Cook, stirring constantly with a wire whip, for 2 minutes. Remove from heat and set aside.
In a large pot or Dutch oven, add water, chicken broth, onions, celery and carrots.
Place over medium high heat and bring to a boil.
Once soup comes to a boil, stir in the cooked butter and flour mixture. Continue cooking for 3 minutes, stirring continuously.
Reduce heat. Stir in cheese. Cook, stirring, until completely melted. Do not allow it to scorch.
Add Tabasco sauce, Worcestershire sauce, cream, lemon zest, mustard, white pepper and broccoli. Return to a simmer, then remove from heat.
Serve hot sprinkled with Cheddar cheese.