Discard the leeks' tough outer leaves, trim the leeks to about 7 inches long, and cut 'em lengthwise into quarters or eighths. In a shallow dish cover the leeks with cold water, soak for 15 minutes, and rub them occasionally to remove any grit. In a heavy skillet, melt butter over moderate heat. Lift the leeks out of the water, and with a bit of water still clinging to them, add them to the skillet. Cook leeks, stirring occasionally, for five minutes, and add broth and zest. Braise leeks, covered, for another 5 minutes, or until very tender, and season with salt and pepper.