Place cashews into a large container and cover with several inches of cool water; let soak, 3 to 4 hours.
Drain cashews and transfer to a food processor. Add lemon juice, olive oil, nutritional yeast, garlic, salt, and basil leaves. Process until thick and smooth, 3 to 4 minutes. Stop to scrape down the sides occasionally.
Transfer cashew mixture to an airtight container. Refrigerate for 1 to 2 hours.