In a large pot, bring 4 quarts of generously salted water to a boil. Meanwhile, melt the butter in a skillet over low heat. Then add the leeks to the skillet, and season them with salt and pepper. Cover the skillet, and cook until the leeks are soft and slightly caramelized -- 5-8 minutes.
Cook the pasta just until al dente (follow package directions).
When the leeks are tender, add the cream, 1/4 cup of the boiling pasta water, and the thyme and lemon zest. Increase the heat, and allow the cream to bubble until it thickens -- about 3 minutes. Drain the pasta. Add the pasta to the skillet, and stir to coat.
Off heat, stir the lemon juice into the pasta. Then divide the pasta between 4 plates. Top each serving with a generous dusting of the cheese and parsley. Enjoy!