Begin by trimming the dark green tops and root ends off the leeks, then slice them in half lengthwise. Rinse thoroughly under cold water to remove any grit trapped between layers. Chop into thin half-moons about 1cm wide.
Place a large skillet over medium-low heat and add the butter. Let it melt gently until it bubbles softly, filling the kitchen with a rich, buttery aroma.
Add the sliced leeks to the skillet, sprinkle with a pinch of salt, and cook slowly for about 15-20 minutes. Stir often; the leeks should turn translucent, soft, and slightly golden at the edges, releasing a sweet, mellow aroma.
While the leeks cook, bring a large pot of salted water to a rolling boil. Add the pasta and cook until just al dente, about 1 minute less than the package suggests. Drain, reserving half a cup of pasta water.
Add the cooked pasta to the skillet with the tender leeks, then pour in the heavy cream. Gently stir to coat the pasta evenly, allowing the sauce to simmer on low for 2-3 minutes until slightly thickened and glossy.
Squeeze the juice of half a lemon into the skillet, stirring to brighten the sauce. If it seems too thick, add a splash of the reserved pasta water and stir until silky and smooth.
Taste the sauce and adjust with salt and freshly cracked pepper as needed. The sauce should be creamy, fragrant with lemon, and coated evenly over the pasta and leeks.
Remove from heat and let rest for a minute or two. Then, transfer to serving bowls and garnish with chopped chives or parsley for a fresh pop of color and flavor.
Enjoy immediately while warm, with the tender leeks, silky sauce, and al dente pasta creating a comforting, elegant dish.
