Bring a large pot of salted water to a rolling boil. Drop in your pasta and cook until al dente, about 8-10 minutes, then drain and set aside.
While the pasta cooks, trim dark green tops from the leeks and slice the white and light green parts thinly. Rinse them well in cold water to remove any dirt, then drain thoroughly.
Heat the frying pan over medium heat and add the butter. Once melted and bubbling softly, add the sliced leeks and a pinch of salt. Cook slowly, stirring occasionally, for about 15-20 minutes until they’re translucent and slightly caramelized, filling your kitchen with a sweet, buttery aroma.
Pour in the heavy cream and stir well, allowing it to warm and thicken slightly, about 3-5 minutes. The leeks will become velvety and rich, coating the bottom of the pan.
Stir in the grated Parmesan cheese, letting it melt into the sauce until smooth. If the sauce seems too thick, add a splash of reserved pasta water to loosen it and create a silky texture.
Add the drained pasta to the pan, tossing gently to coat each strand evenly with the leek sauce. Let it cook together for another minute, allowing the flavors to meld beautifully.
Finish by squeezing fresh lemon juice over the pasta and seasoning with salt and pepper to taste. Give everything a gentle stir, then taste and adjust seasoning if needed.
Serve immediately while warm, garnished with extra Parmesan if desired, and enjoy the velvety, sweet flavors of this comforting leek pasta.