Trim the roots and most, but not all, of the green leaves from the leeks, leaving each leek about 7 inches long. Split down to but not through the base and wash thoroughly.
Bring 3 quarts of salted water to a boil in a pot, add the leeks, and cook until tender, about 15 minutes. Drain and chop.
Meanwhile, peel the potatoes. Cover them with cold water