In a dry pan (no oil) over medium heat, toast the walnuts until slightly brown (this only takes a few minutes). Watch carefully so they don’t burn. This helps to bring out a richer flavor and remove some of their bitterness.
Add all the ingredients to the bowl of your food processor and turn on, scraping down the sides as needed. (It will have some texture and won’t be completely smooth.)
This basil pesto keeps in the fridge for up to 5 days or in the freezer for a couple of months.