With mortar and pestle: Mince basil leaves finely.
Transfer to mortar and crush to fine paste.
Add garlic and work into paste.
Gradually add pine nuts and crush until smooth.
Blend in cheese.
Add olive oil to mixture in slow steady stream, stirring constantly.
With processor: Combine basil and garlic in work bowl and blend to fine paste, scraping down sides of bowl as necessary.
Add pine nuts and cheese and process until smooth.
With machine running, pour olive oil through feed tube in slow steady stream and mix until smooth and creamy; if pesto is too thick, gradually pour up to 1/4 cup warm water through feed tube with machine running.
Transfer pesto to jar.
Cover surface of pesto with film of olive oil about 1/8 inch thick.
Seal jar with tight-fitting lid.
Refrigerate or freeze.
Stir oil into pesto before using.