Put the basil leaves into the processor and process them until they are cut up. Don't let them become a paste.
Remove the basil from the processor and add the garlic. Process the garlic.
Add the pine nuts and process until they are small bead size, about the same size as the garlic.
Return the basil to the processor, and process altogether for a second or two.
Add the Parmesan and pepper, and process until it is all incorporated. You should have pretty much a paste going by now.
With the processor going, slowly start adding the olive oil. You may not need all the oil, or you may need more. You should stop adding oil before you can see it. Looking at the picture will give you a good idea of what it should look like.
You should have about 1 1/2 cups or so of pesto. Refrigerate immediately to prevent spoilage.
To use the refrigerated pesto, remove from the refrigerator and let it come to room temperature.
You can add sun-dried tomato for a Sun-Dried Tomato Pesto.