Step 1Heat the oven to 350 degrees. Spread the walnuts on a baking sheet and toast until lightly browned, 7 to 9 minutes. Chop the nuts and set them aside.
Step 2Cook the spaghetti in plenty of rapidly boiling salted water until al dente, about 7 to 8 minutes.
Step 3Warm the oil in a large skillet, with the garlic and the red pepper flakes. Cook over medium heat until the garlic turns light gold, then add the arugula with the water clinging to its leaves. Season with a few pinches of salt and cook until wilted and tender, about 3 minutes.
Step 4When the pasta is done, scoop it out and add it directly to the pan with a little of the cooking liquid. Add the walnuts and cheese and toss well. Serve with extra-virgin olive oil drizzled over the top.