Season the chicken with salt and pepper. Heat the oil in a heavy bottomed Dutch oven over medium-high heat. Cook the chicken until browned on both sides and remove. Add the sausage and cook until browned, then remove. Sprinkle the flour over the oil, add 2 T butter and cook over medium heat, stirring constantly, until brown, about 10 minutes. Let the roux cool.

Return the Dutch oven to low heat and melt the remaining 3 T butter. Add the onion, garlic, green pepper and celery, cook for 10 minutes. Add Worcestershire sauce, salt and pepper to taste. Cook, stirring frequently for 10 minutes. Add 6 cups hot water and bullion cubes, stirring constantly. Add the chicken and sausage. Bring to a boil, then reduce heat, cover and simmer for 30 minutes. Add frozen broccoli and simmer for another 30 minutes.