With a food processor running add garlic through chute to mince. Scrape down the sides and add basil, parmesan cheese and salt; process until minced, scraping down sides as needed.
With the food processor running, drizzle olive oil through the chute in a steady stream; process just until combined. (recipe note #2) Taste for seasoning and add more salt if needed. Transfer pistou to a small bowl. Cover and refrigerate until ready to serve. (recipe note #3)
Notes
Or make with a mortar and pestle.
If you're making the pistou ahead of time, transfer to a small container and level the surface with the back of a spoon. Add a thin layer of olive oil to preserve its vibrant color; cover and refrigerate for up to one week.