Heat the olive oil in a heavy-bottomed pan over medium heat. When the oil is hot, add the leeks and cook stirring occasionally until wilted, about 5 minutes. Season with salt and cook 5 more minutes, stirring often.

Add a few tablespoons of water to the leeks and add the sausage into small chunks. Stir and cook for about 7 minutes.

While the dressing is cooking, bring a large pot of water to a rolling boil, add the salt and cook the pasta al dente.

Drain the pasta and add it to the pan with the leeks and sausage. Add the milk and cheese and toss over medium heat for one minute. Serve immediately.