Toast the pine nuts in a dry pan over a medium heat until fragrant and golden brown, stirring frequently, about 3 minutes. (Alternatively, bake in the oven on a baking sheet for 5 minutes at 350°F).
Place the pine nuts in the bowl of your food processor and let them cool for a few minutes.
Add Parmigiano cheese and salt, and process until pine nuts are finely ground.
Add basil leaves, garlic, lemon juice, and pepper to the food processor. Process until basil is finely chopped.
Remove to a bowl. Slowly whisk in the olive oil until combined.
Alternatively, you can slowly pour the oil down the food processor chute with the motor running. Do not process more than 10 to 15 seconds or the olive oil may turn bitter.
Serve immediately or cover with a thin layer of olive oil to prevent browning and refrigerate. This will also freeze well.