Put the parsley, walnuts and garlic on a cutting board. With a mezzaluna or sharp knife, finely chop the ingredients. Put the chopped ingredients in a jar and add the Parmigiano cheese, salt, to taste and 1/2 cup olive oil and mix all the ingredients well. Top up with the remaining extra-virgin olive oil.
Cook's Note: Pesto can be served fresh or it can be preserved in the refrigerator or freezer in an air-tight container. If freezing, omit the cheese and drizzle the top with oil. Thaw, then stir in the cheese.