Put the garlic, basil leaves, salt, and pine nuts in a food processor (or use a pestle and mortar if you're a purist). With the motor running, add the extra-virgin olive oil in a thin steady stream. Once you have an even consistency, add the freshly grated Parmigiano Reggiano cheese to the food processor, and puree for a few more seconds.
Pesto can be served fresh or it can be reserved in the refrigerator or the freezer. Do not add the nuts or the cheese before refrigerating or freezing as these two ingredients can spoil. Just process the garlic with the salt, basil and oil, refrigerate or freeze in an airtight container, and add the nuts and cheese just before serving.