Cook the pasta al dente according to package directions, then drain in a colander.
Meanwhile, toast the walnuts in a small dry skillet over medium-high heat until fragrant, stirring frequently, 3 to 5 minutes.
In the pot the pasta was cooked in, heat the olive oil over low heat, add the garlic stirring until soft and fragrant, 3 to 4 minutes (be careful not to burn it). Return the pasta to the pot, add the broth, all but 2 tablespoons of the walnuts, the parsley, salt and pepper and toss to combine, cooking over low heat for 1 to 2 minutes. Add 1/2 cup Parmesan and toss to combine. Arrange 1/2 cup of arugula leaves on each of 4 serving plates. Top each with about 2 cups of pasta. Sprinkle with remaining cheese, the reserved walnuts and more parsley. Serve hot.