Combine all ingredients, except the oil, in the bowl of a food processor. Pulse until the mixture is finely chopped. With the motor running, slowly pour the oil into the feed tube. Use immediately or freeze for up to a month.
Storing Tip: I love to make things ahead and have them at the ready. To store arugula hazelnut pesto, or any of your herb sauces up to 4 days in the fridge, press plastic wrap onto the surface, smoothing out the air bubbles. The wrap will keep it from oxidizing and turning brown.