Bring a large pot of salted water to a boil and cook your pasta until just al dente, about 8 minutes. Drain, reserving a cup of pasta water, and set aside.
While the pasta cooks, slice the leeks thinly, using only the white and light green parts. Rinse well to remove any grit and set aside.
Heat a large skillet over medium-low heat and add the olive oil. Once shimmering, add the sliced leeks and cook slowly, stirring occasionally, for about 10-12 minutes until they soften and develop a golden, caramelized color and sweet aroma.
Stir in the minced garlic and cook for another minute until fragrant, being careful not to let the garlic burn.
Add the chopped spinach to the skillet and stir until wilted, about 2-3 minutes. If the mixture appears dry, splash in a little of the reserved pasta water to loosen and create a glossy sauce.
Return the drained pasta to the skillet, tossing gently to coat it with the leek and spinach mixture. Add lemon zest and a squeeze of lemon juice for brightness, and season with salt and pepper to taste.
Finish with a drizzle of olive oil and toss everything together off the heat. Let sit for a minute to allow flavors to meld, then taste and adjust seasoning as needed.
Serve hot, garnished with extra lemon zest or pepper if desired. Enjoy the tender greens and perfectly cooked pasta with a silky, flavorful coating.