Preheat oven to 350°. Spread walnuts in a single layer in a dry, shallow baking pan and toast in oven about 5 minutes. Set aside to cool. Wash and stem basil and drain thoroughly. In a food processor, combine toasted walnuts, garlic, half of the olive oil and the salt and pepper. Pulse until the mixture is semi-smooth. Add basil and pulse until smooth while adding the remaining olive oil. Do not over-blend or the basil will turn brown. Transfer to an airtight container and chill until ready to use.