Begin by trimming the dark green tops and roots of the leeks, then thinly slice the pale part. Rinse thoroughly in cold water to remove any grit, then set aside.
Heat a large skillet over medium heat and add the butter. Once melted and bubbling softly, add the sliced leeks in an even layer.
Cook the leeks gently, stirring occasionally, for about 20-25 minutes. You'll notice them gradually turning golden and fragrant, developing a smoky, sweet aroma as they caramelize.
While the leeks cook, bring a large pot of salted water to a boil. Add your pasta and cook until al dente, about 8 minutes. Reserve a cup of pasta water before draining.
Once the leeks are golden and fragrant, pour in the heavy cream, stirring to combine. Let it simmer for 2-3 minutes until slightly thickened and creamy.
Drain the pasta and add it directly to the skillet with the cream and leeks. Toss gently to coat the pasta evenly, adding a splash of reserved pasta water if needed to loosen the sauce.
Squeeze fresh lemon juice over the pasta, then taste and adjust seasoning with salt and black pepper. Toss again to combine.
Garnish the finished dish with chopped parsley and a little extra black pepper. Serve immediately while hot, with a bright lemon wedge on the side.