Horseradish Creamed Leeks

In a large bowl of cold water fan out the leaves of the leaks and rinse them well until there is no grit. In a large skillet heat the butter over moderate heat until the foam begins to subside, add the leeks, patted dry, and toss them to coat them with the butter. Add the broth and the cream, bring the liquid to a boil, and simmer the mixture, uncovered, stirring occasionally, for 25 to 35 minutes, or until the leeks are very tender. Transfer the leeks with a slotted spatula to a gratin dish. Stir the horseradish into the liquid remaining in the skillet and season the sauce with salt and pepper. Pour the sauce over the leeks, sprinkle it with Gruyère, and broil the leeks under a preheated broiler about 4 inches from the heat for 2 minutes, or until the cheese is golden.