In a blender, Vitamix, or food processor, combine the oil and garlic.
Once garlic is well chopped, remove half of the mixture and put it aside.
Add salt, pepper, and cider vinegar to the blender bowl. (You can also add anchovies at this point if desired.)
Add 1/2 of the basil and blend until the basil is well incorporated. Continue to blend for a further 20 seconds. (Tip: For greener pesto, blanch the basil leaves, ice and drain prior to making the pesto!)
Add the second half of the basil. As you mix on full speed, slowly add the reserved garlic and oil mixture.
Add the pine nuts and blend until well-incorporated, then continue for an additional 20 seconds.
Remove pesto from the blender and put into a mixing bowl. Fold in the finely grated Parmigiano Reggiano.
Salt to taste and chill until use.