Wash and dry the basil leaves gently — they should be clean but not wet. Toast the pine nuts lightly in a dry pan for 2–3 minutes until fragrant, then let them cool.
Traditionally this next step is done in a mortar and pestle but in these busy modern times, I need my food processor. ;-)
Combine basil, garlic, pine nuts, and a pinch of salt in a food processor. Pulse a few times until finely chopped. Add the cheeses and pulse again. With the machine running, slowly stream in the olive oil until the mixture becomes smooth and creamy. Avoid over-blending — too much heat can darken the basil and alter the flavor.
Taste and adjust:
Add more salt or cheese as desired.
Toss immediately with hot pasta (reserving a little pasta water to loosen the sauce), spread on toasted bread, or drizzle over grilled vegetables or meats.