Blanch grape leaves by placing them in a pan and covering with boiling water. Let sit for 3-5 minutes.
Heat the walnuts in a small frying pan over medium heat, stirring frequently, until they smell "toasty." (Do not let them burn.)
Combine blanched grape leaves, basil, garlic, Parmesan, olive oil, and toasted walnuts in the bowl of a food processor. (If you use a blender, start with about half the grape leaves and add the others after the first half has been pureed.) Blend to a smooth paste.