Trim off the dark green tops and root end of the leeks, then slice the white and light green parts into thin half-moons. Rinse thoroughly in cold water to remove any grit, then drain well.
Bring a large pot of salted water to a rolling boil, then add the pasta and cook until just al dente, about 1 minute less than package instructions. Drain, reserving about half a cup of pasta water, and set aside.
Heat a large skillet over medium-low heat and add the butter. Once melted, add the sliced leeks with a pinch of salt, stirring gently. Cook slowly, stirring occasionally, until they soften and turn a light golden brown, about 15 minutes. They should smell sweet and smoky, not burnt.
Add the crushed garlic to the skillet with the leeks and cook for about 30 seconds until fragrant, stirring constantly to prevent burning.
Pour in the heavy cream, stirring to combine. Raise the heat slightly to medium and let the mixture simmer gently, stirring occasionally, until the sauce thickens slightly and becomes glossy, about 3-4 minutes.
Return the cooked pasta to the skillet, tossing to coat it thoroughly with the leek and cream sauce. If the sauce feels too thick, add a splash of the reserved pasta water to loosen it and achieve a silky texture.
Squeeze the juice of half a lemon over the pasta, then toss gently to combine. Taste and season with salt and pepper as needed.
Serve immediately while warm, garnished with a little extra black pepper if desired. The sauce should be glossy, and the leeks tender and caramelized.
