Cook ground beef, onion, celery, and garlic in a large Dutch oven over medium-high heat, stirring until beef crumbles and is no longer pink and vegetables are tender. Drain, if desired.
Stir in ham, oysters, and parsley. Cook 7 minutes or until oysters are done. Gently fold in stuffing mix, salt, and pepper.
Spoon stuffing mixture into a lightly greased 13- x 9-inch baking dish. Serve immediately or cover and chill until ready to serve. Bake, covered, at 350º for 35 minutes or until thoroughly heated.