In a food processor mince the basil, garlic, salt and pepper together until very fine, almost a puree. Mix in a small bowl or cup with 1 tablespoon of the olive oil. Make a deep horizontal slit in the side of each of the scallops, but don't cut all the way through. Fill each scallop with about a teaspoon of the basil mixture; close. Pour the remaining oil onto a plate or pan and turn the scallops in it. Let sit while you preheat Grill or BBQ; it should be very hot before grilling, with the rack about 4 inches from the heat source.
Place the scallops on the grill (don't pour the remaining oil over them, as it will catch fire), and grill 2 to 3 minutes per side, no more. Serve immediately, with lemon wedges.