Add basil, nuts, garlic, lemon juice, nutritional yeast, sea salt and blend/mix in a food processor on high until a chunky paste forms. You should still see very small pieces of walnut in the mix.
Drizzle in olive oil until paste becomes smooth and loose. Scrape down sides as needed.
Adjust flavor to your taste. Add more nutritional yeast for a cheesy flavor, more nuts for nuttiness, more garlic for bite, or more lemon juice for acidity.
Store covered in the refrigerator up to 1 week. After that, pour into ice cube molds, and freeze for up to 3 months.