Bring a large pot of salted water to a rolling boil. Add the pasta and cook until just shy of al dente, about 1 minute less than package instructions. Reserve 1 cup of starchy pasta water before draining.
While the pasta cooks, slice the leeks thinly, then rinse thoroughly to remove any grit between the layers. Drain well and set aside.
Heat the large skillet over medium-low heat. Add the olive oil and gently sauté the sliced leeks, stirring often. Cook slowly for about 8-10 minutes until they become soft, translucent, and fragrant with a subtle sweetness.
Add the minced garlic to the skillet and cook for about 30 seconds until it releases a fragrant aroma, being careful not to let it burn.
Toss in the fresh spinach and stir until it wilts, about 2-3 minutes. The leaves will darken and shrink significantly, creating a vibrant, earthy aroma.
Add the drained pasta to the skillet and pour in about 1/4 cup of the reserved pasta water. Toss everything together until the pasta is coated in the greens and a silky sauce forms. Add more water if needed to loosen the mixture.
Remove the skillet from heat and stir in the lemon zest. Squeeze a little lemon juice over the pasta for brightness. Season with salt and pepper, tasting and adjusting as needed.
Let the pasta rest off the heat for a minute to allow flavors to meld. Give it a final toss and serve immediately, garnished with extra lemon zest or a drizzle of olive oil if desired.
