Start by filling your large pot with water, adding a generous pinch of salt, and bringing it to a rolling boil. Meanwhile, peel and thinly slice the leeks, rinsing them well to remove any grit. Set aside.
Heat the olive oil in a deep skillet or wide pan over medium heat until it shimmers and begins to smell fragrant. Add the sliced leeks and a pinch of salt, then cook gently, stirring occasionally, until they turn translucent and slightly caramelized, about 8 minutes. You should hear a gentle sizzle and see the leeks soften and turn golden at the edges.
While the leeks cook, add your pasta to the boiling water. Cook until just al dente—about 1-2 minutes less than package directions. Reserve a cup of starchy pasta water before draining the pasta and set aside.
Push the cooked leeks to one side of the pan. Add the minced garlic to the empty space and sauté for about 30 seconds, stirring constantly, until it becomes fragrant and slightly golden. Be careful not to burn it—if it browns too quickly, lower the heat.
Stir in the fresh spinach, a handful at a time, until it wilts and turns bright green—about 1-2 minutes. The spinach releases moisture and infuses the aroma of garlic and leek, creating a vibrant base for the dish.
Drain the pasta and add it to the skillet with the sautéed vegetables. Toss everything together, adding a splash of the reserved pasta water to loosen the mixture and help the flavors cling to the noodles. Cook for another minute until everything is heated through and slightly glossy.
Finish by squeezing the lemon juice over the pasta and sprinkling the freshly grated Parmesan on top. Toss gently to combine, allowing the cheese to melt into the warm pasta and brighten the dish with a fresh citrus note.
Taste and adjust with more salt, pepper, or lemon if desired. Serve immediately, garnished with extra Parmesan if you like. The dish should be vibrant, creamy, and just tender—ready to enjoy!