Pulse pine nuts, garlic, lemon juice, and 2 tablespoons olive oil in a food processor until chopped.
Add avocado, basil, salt, and pepper. Process until smooth.
Avocado Pesto should be refrigerated immediately after making and only kept in the refrigerator for 2-3 days. If stored longer, there is a risk that the raw garlic, which is extremely low acidity, may produce botulism, a serious toxin.