In a large pot of salted water, cook the kale until tender, 4 to 5 minutes. Using a slotted spoon, transfer the kale to a colander and rinse with cold water. Add the pasta to the pot and cook until al dente. Drain, reserving 1/3 cup of the pasta cooking water. Return the pasta to the pot.
Meanwhile, squeeze the kale to remove the excess water. In a food processor, combine the kale, walnuts, garlic and parmesan until almost smooth; season with salt and pepper. With the machine running, add the olive oil.
Add the pesto to the pasta, along with enough pasta cooking water to loosen the pesto as necessary. Serve sprinkled with more parmesan.