In a large pan bring water to boil and add drumstick, cook on medium heat for 45 minutes. Take out the drumstick and add broccoli florets; cook for about 15 minutes until broccoli are soft. Add salt and peeper (or some bullion, whatever you prefer). On a small pan melt butter and add flour, mix it and keep it on the low heat. Add about 1/2 cup of the hot water from the large pan (the one with broccoli) to butter and flour; mix it and quickly add all of it to the large pot with soup and broccoli florets. Mix all ingredient together very well, we do not want clumps to form from flour. Add half & half and still mix it for few seconds; cook on low heat for about 5 - 10 minutes. Add cheese. On the small cooking pan cook chopped bacon until it reaches the crispiness. Serve soup with some bacon on top and bread. In the end the chicken drumstick can be chopped and add it to the soup.