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Bring small pot salted water to boil. Cook pappardelle according to package directions.
Add kale and garlic to food processor and mix until kale is finely chopped. Add walnuts and process again until nuts are chopped. Add cheese, pulse again; then start adding olive oil while food processor runs on low. Taste and adjust seasoning with sea salt and ground pepper. Eat immediately or store in glass jar in fridge about 4 days.
Drain pappardelle, reserving ½ cup pasta water. Toss pappardelle with pesto, 1 tablespoon at a time, until well coated. Slowly add a bit of pasta water to loosen up sauce, if desired.