Prepare the kale by rinsing and removing the stems.
Toast the walnuts in a dry skillet over medium heat until fragrant.
In a food processor, combine kale, toasted walnuts, garlic, and Parmesan cheese.
While processing, slowly drizzle in the olive oil until smooth.
Add lemon juice, salt, and pepper, adjusting to taste.
Cook the pasta according to package instructions until al dente.
Toss the cooked pasta with the kale pesto, adding reserved pasta water as needed.
Serve immediately with extra Parmesan and a drizzle of olive oil.