Place the walnuts, basil, garlic, salt and pepper in a food processor and pulse until chunky.
Slowly drizzle in the olive oil and pulse till smooth.
Finish with a dash of lime juice.
You should end up with a little less than a cup of pesto. Its best to use it right away or it starts to darken. However, if you need to store it, use the smallest possible container, top with olive oil and store in the refrigerator for up to a week.