Place butter, oil, cheese, and parsley into a blender. Cover, and puree until smooth. Season with salt and pepper to taste.
Butterfly the shrimp leaving the shell on. Starting at the head, cut almost all the way through the flesh, down the center of the shrimp's back and to the tail. Open the two sides and spread them out like an open book. Dip the shrimp into the butter mixture, or if the mixture is too thick rub it onto the shrimp.
Place the shrimp shell side down on the preheated grill. Cook the shrimp until they are bright pink on the outside and the meat is no longer transparent in the center, about 2 to 3 minutes per side.
