Place the oregano, basil leaves and garlic in a food processor. Whirl until pureed. Add the walnuts; whirl for 30 seconds. With the food processor running, slowly pour through the feed tube all but 2 tablespoons of the olive oil. Reserve the 2 tablespoons of oil for basting the scallops. Transfer the herb, walnut and oil mixture to a bowl; cover and refrigerate until ready to serve.
Prepare a grill with hot coals with the grill rack 4 inches from the coals, or preheat a broiler with the broiler pan 4 inches from the heat. Drizzle the reserved 2 tablespoons of olive oil over the scallops in a bowl and season with the salt and pepper; toss lightly to coat the scallops evenly. Thread the scallops on several metal skewers.
Grill or broil the scallops for 3 to 4 minutes or until centers are opaque, turning once.
To serve, stir the Parmesan cheese into the herb mixture in the bowl to complete pesto. Spoon some pesto over the scallops on each dinner plate. Pass the remaining pesto. Serve with crusty bread and a cherry tomato salad if you wish.