Slice the leeks thinly, about 0.5 cm wide, and rinse them thoroughly under cold water to remove any grit. Drain well.
Bring a large pot of salted water to a boil, then add the pasta. Cook until al dente, about 8-10 minutes, then drain, reserving a cup of pasta water.
While the pasta cooks, melt the butter in a large skillet over medium-low heat. Add the sliced leeks and a pinch of salt, stirring gently.
Cook the leeks slowly, stirring occasionally, until they turn golden and soft, about 15-20 minutes. The aroma will become sweet and buttery, and the leeks will soften into tender strands.
Reduce the heat to low, then pour in the heavy cream. Stir to combine, letting it warm through and slightly thicken, about 2-3 minutes.
Add the cooked pasta to the skillet with the leeks and cream. Toss gently to coat the noodles evenly, adding a splash of reserved pasta water if needed to loosen the sauce.
Grate Parmesan cheese over the pasta and stir until melted into the sauce. Squeeze in lemon juice and season with salt and black pepper to taste.
Remove from heat and let sit for a minute to allow flavors to meld. Taste again and adjust seasoning if necessary.
Serve immediately, garnished with extra Parmesan or herbs if desired. Enjoy the creamy, fragrant pasta while warm.
