Trim off the root ends and dark green tops of the leeks, then slice them thinly into half-moon shapes. Rinse thoroughly under cold water to remove any grit.
Bring a large pot of salted water to a boil, then add your pasta. Cook until al dente, about 8-10 minutes, then drain, saving a cup of pasta water for later.
While the pasta cooks, heat the large skillet over low to medium-low heat and add the butter. Let it melt gently until it starts to shimmer and smells slightly nutty.
Add the sliced leeks to the skillet. Stir gently to coat them in butter, then cook slowly over low heat, stirring occasionally. Watch as they soften and gradually turn a deep golden color, filling your kitchen with a sweet, caramelized aroma—this takes about 20-25 minutes.
Once the leeks are beautifully golden and fragrant, pour in the heavy cream. Stir gently and let it warm up, allowing the sauce to thicken slightly and coat the leeks with a silky texture, about 3-5 minutes.
Add the drained pasta to the skillet with the leek cream sauce. Toss everything together, stirring gently to coat the noodles evenly. If the sauce feels too thick, add a splash of the reserved pasta water and stir until silky.
Finish by stirring in the lemon juice, then sprinkle with finely grated Parmesan cheese. Season with salt and pepper to taste, adjusting until the flavors are balanced and bright.
Remove from heat and let the pasta rest for a couple of minutes. Serve hot, garnished with extra cheese or herbs if desired, and enjoy the rich, silky textures of this slow-cooked leek pasta.
