In the bowl of a food processor, combine pine nuts, basil leaves, parmesan cheese, lemon juice, garlic, and kosher salt. Pulse the mixture until it is finely minced, stopping to scrape down the sides of the bowl as needed.
Switch the food processor to its lowest setting and slowly drizzle in the olive oil in a thin, continuous stream. Continue blending until all ingredients are fully incorporated; it’s okay if there are a few small pieces of basil remaining.
Transfer the pesto to an airtight container and store it in the refrigerator for up to three days.