How to Make It
In a small skillet, toast the walnuts over moderately low heat until golden, about 5 minutes. Finely chop 1/2 cup of the walnuts; coarsely chop the rest for garnish.
In a food processor, pulse 2 cups of the arugula until finely chopped; scrape into a large bowl and stir in the 3/4 cup of olive oil, the garlic, grated cheese and finely chopped walnuts. Season the pesto with salt and pepper.
In a large pot of salted boiling water, cook the pappardelle until al dente. Drain the pasta and add to the pesto in the bowl. Add the zucchini and toss to evenly coat. Stir in the lemon juice and the remaining 2 cups of arugula and season with salt and pepper. Transfer the pasta to a platter, drizzle with olive oil and garnish with the coarsely chopped walnuts and cheese shavings.