Bring a large pot of well-salted water to the boil. Add the pasta and cook according to packet instructions until al dente. Before draining, reserve ½ cup of the pasta cooking water, then drain.

While the pasta cooks, place the kale, walnuts, garlic, lemon juice, and salt into a food processor. Pour in the olive oil and blend until everything starts to come together. Scrape down the sides with a rubber spatula, then continue to blend to your desired consistency. Taste and adjust salt and lemon juice as needed.

Return the drained pasta to the saucepan over low heat. Add a couple of tablespoons of the reserved pasta water to loosen, then add the pesto and toss well to combine. Add a little more pasta water as needed until every piece of pasta is well coated. Taste and adjust salt and lemon juice once more. Serve immediately with extra lemon wedges on the side.