Add the basil, parmesan cheese, cashews, lemon juice, garlic, salt and pepper to the food processor, and blend until a paste starts to form.
While the food processor is running, slowly drizzle in the olive oil until ingredients are well combined. Scrape down the sides as you go, if necessary.
Adjust seasoning and consistency, if desired (see notes below). Store in a sealed container in the refrigerator and eat within a week. See post for freezing instructions.
