Bring a large pot of salted water to a boil and cook your pasta until just shy of al dente, about 8 minutes. Reserve a cup of pasta water before draining, then set the pasta aside.
While the pasta cooks, trim the roots and dark green tops from the leeks, then slice them thinly. Rinse them thoroughly under cold water to remove any grit—this helps keep them tender and sweet.
Heat the large skillet over medium-low heat and add 2 tablespoons of olive oil. Once shimmering, add the sliced leeks. Cook slowly, stirring occasionally, until they turn a deep golden color and release a sweet aroma, about 15-20 minutes.
2 large leeks
When the leeks are nicely golden, add the minced garlic and cook for about 1 minute until fragrant, stirring constantly to prevent burning.
2 large leeks
Drop the drained pasta into the skillet with the leeks and garlic. Pour in a splash of reserved pasta water and toss gently to help the flavors meld, cooking for another 2 minutes.
Gradually add the fresh spinach in batches, stirring until each addition wilts and turns vibrant green, about 1-2 minutes per batch. The greens should be tender but still bright.
2 large leeks
Squeeze fresh lemon juice over the mixture, then drizzle with a little more olive oil. Season with salt and pepper to taste, tossing gently to combine all the flavors.
Remove from heat and let the pasta rest for a minute. Serve hot, drizzled with extra olive oil and a squeeze of lemon if desired, enjoying the tender, flavorful greens and caramelized leeks.