Fill a large heavy-bottomed pot or Dutch oven with heavily salted water and bring it to a boil. Add the pasta and cook according to package directions until al dente. Scoop out 1 cup of pasta water and set it aside. Drain the pasta and drizzle with olive oil to prevent sticking.

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

Heat the olive oil in the now-empty pot over medium-high heat. Add the zucchini and season with 1 ½ teaspoons salt and ½ teaspoon black pepper. Cook, stirring occasionally, until the zucchini releases liquid, the liquid cooks off, and the zucchini becomes jammy but not browned, 12 to 15 minutes. You’ll know it’s ready when the zucchini begins to stick to the bottom of the pot. Turn the heat off.

Meanwhile, place the cottage cheese, basil, most of the lemon zest and juice (you’ll use the rest later), the remaining 1 teaspoon salt, and several grinds of black pepper in a food processor. Process, scraping down the bottom and sides of the bowl halfway through, until smooth, about 1 minute.

Set the pot of zucchini on low heat. Add the pasta and stir to distribute the zucchini. Add the cottage cheese mixture and ½ cup of the pasta water and stir, adding more as needed, until a creamy sauce coats the noodles. Taste and add more salt, pepper, or lemon juice as desired.

Divide into bowls and top with more basil, the reserved lemon zest, and a drizzle of olive oil.