Heat a large skillet over medium heat and add the olive oil, allowing it to shimmer as it warms.
Add the sliced leeks to the skillet and cook, stirring occasionally, for about 5-7 minutes. They should become soft, translucent, and slightly golden around the edges, releasing a sweet aroma.
Push the leeks to one side of the pan and add the minced garlic to the cleared space. Sauté for about 30 seconds until fragrant, stirring constantly to prevent burning, until it turns a light golden color.
Meanwhile, bring a large pot of salted water to a rolling boil. Add the pasta and cook until just al dente, following package instructions, about 8-10 minutes. Drain, reserving a cup of pasta water.
Add the fresh spinach to the skillet with the leeks and garlic, in batches if needed, and cook for about 2-3 minutes until just wilted and vibrant green. The greens should be tender but still bright.
Pour the cooked pasta into the skillet with the greens, tossing everything together to coat in the flavorful oil and vegetables. If the mixture seems dry, add a splash of the reserved pasta water and stir until the sauce becomes glossy and slightly loosened.
Finish by adding the lemon zest over the pasta, then season with salt and freshly ground black pepper to taste. Toss gently to combine, and taste for balance—add more salt or pepper if needed.
Serve immediately in warm bowls, garnished with extra lemon zest if desired. The dish should be fragrant, with tender greens, al dente pasta, and a bright, fresh flavor.
