In a large pot over high heat, combine the chicken broth and the broccoli. Cook about 3 to 5 minutes, or until tender. Set aside. In a large skillet, saut E the onions in the butter or margarine for about 5 minutes or until lightly browned. Add the garlic, crawfish or shrimp, hot pepper sauce and Creole seasoning. Saute another 5 minutes and add to the broccoli and broth.
In a separate bowl, mix together the cream of chicken soup, the cream of celery soup, and the milk. Mix the cornstarch and cold water and stir into the soup mixture. Mix well. Add mixture to the broccoli and broth. Cook over medium heat, stirring constantly until thick and bubbly. Stir in cheese. Reduce heat to low and stir until cheese is blended. DO NOT BOIL.