In a food processor add the basil, walnuts, garlic, avocados, lemon juice, and seasonings. Pulse until creamy.
With food processor on high, slowly drizzle in the olive oil, scraping sides of bowl as needed.
Adjust the seasoning as needed. Store pesto in jars or airtight container.
Notes
Since this pesto is made with avocados, slight darkening might occur on top layer. It's completely edible, but if color bothers you gently scrape off top layer and discard.