Trim off the roots and remove any withered leaves. Carefully slit the leeks lengthwise on either side to within 1 1/2 inches of the base and gently fan out the leaves. Wash thoroughly under running water in order to remove all the grit and sand. Cut off a portion of the green tops to leave the leeks about 7 inches long. In a baking dish that can be placed on the stovetop, place the leeks in two or three layers. Pour in enough boiling water to come two thirds of the way up the layers. Add the butter and salt. Partially cover the dish, leaving a small space to allow steam to escape. Maintain the liquid at a fairly fast boil. As the leeks soften, the water will just cover them. In 30-40 minutes, the white part of the leeks will be tender when pierced with a knife. The liquid should almost be evaporated. Transfer the leeks to a baking dish and pour the remaining cooking juices over them.
Thirty minutes before serving, cover loosely with foil and set in the middle of a 325-350° oven for approximately 20 minutes. The leeks should be a light golden color. Sprinkle with parsley and serve.