False. Yes, green beans stewed until they are gray beans may have lost many of their nutrients―mostly vitamins, which are water soluble, says chef and nutritionist Nancy Berkoff, R.D., a consultant with the Vegetarian Resource Group. But important minerals like iron and potassium don’t break down easily in water. “All vegetables, overcooked or not, are a good source of fiber, too,” says Berkoff. Your best bet: Steam them lightly to the desired consistency.