1. Cut off the root ends of the leeks and trim the tough green tops of the leaves. Cut the leeks crosswise in half and then lengthwise in half again. Cut each quarter in lovg, very thin strips and place in a large bowl of cold water to soak.
2. Put the sausage and 1/4 cup water in a 10- to 12- inch saute pan and place it over medium-high heat. Break up the sausage with a woden spoon and cook until all the water is evaporated and the sausage begins to brown lightly.
3. Fill a pot for the pasta with at least 4 quarts water and place it over high heat.
4. Lift the leeks out of the water, so that any dirt remains in the bottowm of the bowl. Discard any fat the sausage may have released, add the butter and leeks to the saute pan, and season with salt and pepper (bear in mind that the sausage is already seasoned). Turn the heat down to medium-low and cover the pan. Cook, stirring occasionally, until the leeks are wilted and very tender, 15 to 20 minutes.
5. After the leeks have been cooking for about 12 minutes and the water for the pasta has come to a boil, add 1 T. salt to the boiling water, put in the pasta, and stir well.
6. While the pasta and the leeks are cooking, grate the cheese.
7. When the leeks are tender, uncover the pan and raise the heat to medium-high. Cook, stirring, until all the water the leeks release evaporates. Remove from the heat.
8. When the pasta is al dente, drain it and toss it with the sauce and grated cheese. Serve at once.