Add the basil, garlic, walnuts, cheese, and salt to your food processor bowl. Pulse several times until everything is finely chopped, pausing to scrape down the sides with a spatula as needed.
With the food processor running, add oil through the feed tube in a slow steady stream. Continue processing until smooth. Use right away, or store following the directions in the recipe notes.
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Notes
Transfer the finished pesto to an airtight container for refrigerator storage (keeps up to one week). To maintain its vibrant green color, smooth the surface and pour a thin layer of olive oil on top. For longer storage, freeze for up to 6 months. A convenient method is to freeze portions in an ice cube tray, then transfer the frozen cubes to a freezer bag for easy use.
For a stronger garlic flavor, increase to 2 or 3 cloves.