Bring a large pot of salted water to a boil.
Meanwhile, heat 2 tablespoons of olive oil or butter in a heavy bottomed dutch oven or large pot over medium high. Add leeks and sweat for about 5 minutes, or until soft and almost translucent, stirring occasionally. Season generously with kosher salt.
Add garlic and sauté until fragrant, about a minute.
Add grated zucchini and cook down for about 15-20 minutes, or until its saucy, releases most of its moisture and the mixture reduces by about half. Season generously with kosher salt.
When the zucchini has been cooking for a few minutes, cook the pasta just shy of al dente, as it’ll finish cooking when you toss it into the zucchini mixture. Reserve 2 cups of the pasta water - you’ll use this for your sauce.
When the zucchini has cooked down, add the cooked pasta, goat cheese, grated Parmesan, lemon zest and juice, and 1 cup of the reserved pasta water. Stir until combined and creamy, tasting to make sure the pasta is cooked to your liking. Season to taste with salt and pepper, and add more pasta water to loosen up the sauce as needed.
Serve with generous amounts of grated parmesan, chopped fresh herbs, cracked black pepper, and crushed red chili flakes, if desired.