Place half of the walnuts, parsley, cheese and garlic in food processor; process until finely chopped.
With motor running, slowly pour in half of the oil; purée until smooth. Transfer to bowl and repeat with remaining ingredients, making a total of 2 batches. Season with salt and pepper; set aside. (Makes approximately 4 cups).
Cook pasta in boiling salted water until al dente, about 3 to 4 minutes. Drain, reserving some of the cooking water. For each serving, toss 2 cups cooked pasta with 1/4 cup Walnut Pesto adding some of the reserved cooking water as required to thin the pesto; toss well to coat evenly.
Transfer to warm pasta bowl; sprinkle with 1 tablespoon chopped walnuts and shaved or grated cheese, as desired. Serve immediately.