Every spring when arugula is bountifully available at the farmers' market I buy some. It's good in salads but I am still partial to the pesto. Here is the recipe I've been using for years. I think I found it on the FoodTV Web site. I've never tried it with toasted walnuts but I'm sure it is equally tasty.
Recipe: Arugula (rocket) pesto:
4 cups packed fresh arugula
1/2 head of minced garlic
Salt and freshly ground pepper
1 cup pure olive oil
3 tablespoon pine nuts, toasted
1/2 cup freshly grated Parmesan
Prepare an ice water bath in a large bowl, and bring a large pot of water to a boil. Put the arugula in a large sieve and plunge it into the boiling water. Immediately immerse all the arugula and stir so that it blanches evenly. Blanch for about 15 seconds. Remove, shake off the excess water, then plunge the arugula into the ice water bath and stir again so it cools as fast as possible. Drain well.
Squeeze the water out of the arugula with your hands until very dry. Roughly chop the arugula and put in a blender. Add the garlic, salt and pepper to taste, olive oil, pine nuts. Blend for at least 30 seconds. In this way the green of the arugula will thoroughly color the oil. Add the cheese and pulse to combine. The pesto will keep several days in a tightly sealed container in the refrigerator. Serve w/ pasta or in any dish requiring pesto.