Combine potatoes, leeks or onions,vegetable broth, and water in a large heavy pot or saucepan. Cover and bring to a boil over medium-high heat
Reduce heat and simmer 35 to 45 minutes, or until vegetables are tender. Without draining off broth, mash vegetables in the pan with a vegetable (potato) masher until they are fairly smooth.
If they do not mash easily, soup has not cooked long enough. Let it simmer 10 to 15 minutes longer.)
Add cream, butter, salt, and pepper. Heat soup just to the boiling point. (Do not boil.) Serve in bowls and sprinkle each serving with chives.