Cook the Pasta: Fill a large pot with heavily salted water and bring it to a boil. Add the pasta and cook according to package directions until al dente. Reserve 1 cup of pasta water, then drain the pasta and drizzle with olive oil to prevent sticking.

Prepare the Zucchini: While the pasta cooks, trim the zucchini and grate them through the large holes of a box grater.

Cook the Zucchini: In the empty pot, heat olive oil over medium-high heat. Add the grated zucchini, seasoning with 1 1/2 teaspoons of salt and 1/2 teaspoon of black pepper. Cook, stirring occasionally, until the zucchini releases liquid and becomes jammy (12 to 15 minutes). It should start sticking to the pot.

Make the Sauce: In a food processor, blend the cottage cheese, most of the lemon zest and juice, the remaining 1 teaspoon of salt, and several grinds of black pepper until smooth (about 1 minute).

Combine: Set the pot of zucchini to low heat, add the cooked pasta, and stir to distribute. Add the cottage cheese mixture and 1/2 cup of reserved pasta water, stirring until creamy. Adjust seasoning with salt, pepper, or lemon juice as needed.

Serve: Divide into bowls, topping with more basil, reserved lemon zest, and a drizzle of olive oil.