1. Peel potatoes and quarter. Cut cabbage into 1-inch squares. In a 5- to 6-quart kettle cover potatoes and cabbage with salted cold water by 2 inches and simmer until very tender, about 30 minutes.
2. While vegetables are simmering, cut pale green and white parts of leeks into 1/2-inch pieces and in a bowl of cold water wash leeks well. Lift leeks from water into a colander to drain. In a saucepan simmer leeks in broth, covered, until very tender, about 20 minutes. Drain leeks in a sieve set over a bowl and reserve cooking liquid.
3. Drain potatoes and cabbage in a colander and transfer to a large bowl. With a potato masher mash mixture. Stir in leeks, adding some of reserved cooking liquid to thin potatoes if desired. Season potatoes with salt and pepper. Potatoes may be made 1 day ahead and chilled, covered. Reheat potatoes, covered, in a 350°F. oven about 30 minutes.