Cook pasta per package directions. Reserve 1/2 cup cooking water, drain, and return pasta to pot.

While pasta cooks, in a food processor, pulse scallions and 3 cups kale to finely chop. Add cottage cheese, Parmesan, and 1/2 teaspoon each salt and pepper; pulse to combine.

Scrape down sides, then gradually add oil and puree until smooth.

Toss pasta with the sauce to coat, then toss with remaining 3 cups kale, adding reserved pasta water as necessary to help kale wilt. Serve topped with additional Parmesan and freshly cracked pepper.