In the bowl of a food processor, combine the basil, garlic, and pine nuts. Pulse until coarsely chopped—this step should not take long. Add cheese and pulse one or two times to mix.
With the machine running, slowly add the oil and process until it is fully incorporated and smooth. Start with half a cup and only add more if needed. Scrape down the sides once or twice during this process.
Remove to a container and season with salt and pepper if necessary. This tastes delicious mixed into hot pasta. Reserve a little of the hot pasta water and mix into the pasta to thin out the pesto.
Freezing tips for basil: In a food processor, pulse the basil and oil until almost smooth. Place tablespoons of chopped basil into ice cube trays and freeze. Use to flavor soups, sauces, or spreads. The pesto can be frozen in the same manner as well.
If not using immediately, cover the surface with plastic wrap and refrigerate for up to 2 days.