Bring a large pot of salted water to a boil. Add the potatoes and cook 10 minutes, then add the broccoli and pasta and cook as the pasta label directs.
Meanwhile, melt the butter in a large skillet over medium heat. Add the leeks, 1 1/2 teaspoons salt, and pepper to taste. Cook until soft, about 7 minutes.
Put the lettuce in a colander. Reserve 1 cup cooking water, then drain the pasta, broccoli and potatoes over the lettuce to wilt it. Return the pasta and vegetables to the pot.
Add the leeks to the pot and stir in enough of the reserved cooking water to moisten. Stir in the cheeses and season with salt and pepper. Top with more parmesan.
Photograph by Antonis Achilleos
Courtesy of Food Network Magazine