Prepare charcoal fire in grill, and let burn 10 to 15 minutes. Sprinkle wet hickory chips over gray-white coals. Cover grill with lid.
Sprinkle a thin layer of rock salt in an aluminum foil-lined 13- x 9- x 2-inch pan. Arrange oysters (in shells) over rock salt; sprinkle oysters with 1/8 teaspoon salt and pepper.
Combine butter, green onion, and chopped parsley; dot each oyster with butter mixture. Combine cornflake crumbs and cheese, and sprinkle over butter mixture.
Place pan on grill 4 inches from hot coals and wet hickory chips. Cover grill with lid. Grill 20 minutes or until crumbs are browned and oyster edges curl. Garnish with parsley sprigs.
Note: Rock salt is used to hold shells upright and to keep oysters hot.