Pulse toasted pine nuts in a food processor until they're completely broken down. Stop to scrape down the sides of the bowl with a spatula from time to time.
Add olive oil and garlic and pulse until garlic is finely chopped.
Chop basil very roughly — just run a knife through it once or twice to cut most of the leaves into halves or thirds — then add to food processor and pulse, stopping every 15 seconds to push the leaves down with a rubber spatula, until basil is entirely worked into the oil.
Pulse for another few seconds, and then stop to prevent turning the basil brown.
Pour pesto base into a bowl and add grated cheese and salt.
Stir to combine, then taste and adjust seasoning as needed.
Leave the sauce thick to toss with cooked pasta and a little pasta cooking water.
To use the pesto as a garnish for grilled or roasted meats, fish and vegetables, thin it out with 2 to 3 more tablespoons olive oil until it’s the consistency of a loose paste.
To store leftovers, pour a little more olive oil over the pesto to cover.
Refrigerate in an airtight container for up to three days.