Trim the garlic scapes by cutting just below the bulb. Discard the bulb/tip and cut the scapes in about 1" pieces.
In a food processor, add the scapes, walnuts, yeast, lemon juice, salt and pepper. Process by pulsing until the mixture begins to break down. Scrape the bowl down.
With the processor running, slowly add all the olive oil. Continue to process until all the ingredients are incorporated and broken down, about 30-45 seconds, stopping to scrape down the bowl as needed.
Store in a covered container in the fridge and enjoy within a week. Also, you can freeze the pesto in a jar or in an ice-cube tray. Once frozen, in the ice-cube tray, remove and place in a ziplock bag in the freezer.