In a food processor, add walnuts, arugula, salt and garlic. Pulse until walnuts are ground fine. With the motor running, drizzle in the olive oil until a creamy consistency is reached. Adjust the amount of olive oil to suit your own taste.
Makes about 1 cup. Serve immediately or store in the refrigerator for 3 days. To prevent the pesto from turning brown in the fridge, lay plastic wrap down right on the surface, thus preventing exposure to air.