Remove fibrous stalks from the broccoli and break up remaining flowerettes into small pieces.
Place water and broccoli in pot and cover. Bring to boil and simmer until almost tender; about 5 minutes.
Do not drain the broccoli. Add both cans of soup and stir gently so as not to break up the broccoli. Return the cover and simmer about 5 minutes to allow flavors to blend.