Heat a small skillet over medium-high heat and add the walnuts. Shake them in the skillet continuously for 1-2 minutes as you toast them. Once they are lightly toasted remove from the heat and set aside.
Use a fork to remove the sun-dried tomatoes from the oil and place them in the bowl of your food processor.
Pour the oil in a measuring cup and add additional olive oil to it (if needed) to make it ¾ cup of oil. Set aside.
Add the Parmesan cheese, toasted walnuts, garlic, salt and red pepper flakes to the food processor.
Lock the lid in place and turn on the food processor. As the motor is running begin slowly pouring the oil in. You can pause the food processor during this process and scrape the sides down before resuming until you reach a rough texture, not smooth but without large chunks of tomato.
Add the pesto to a dish, eat with bread or crackers, or store in the refrigerator for up to 1 week.