Bring a medium pot of water to a boil. Add a large pinch of salt, and the basil. Blanch for 2 minutes. Drain, and run under cold water to stop the cooking. Drain again, squeezing out excess liquid.
Transfer to a food processor, and add garlic, pine nuts, cheese, and oil. Process until smooth, about 2 minutes. Transfer to a bowl. Cover with plastic wrap, press plastic wrap directly onto the surface of the pistou.
Will keep, refrigerated, for up to 1 week. Return to room temperature before using.