Cook cabbage in boiling water just until the leaves fall off head. Cut out the thick vein from the bottom of 12 large leaves, making a V-shaped cut; set aside. (Refrigerate remaining cabbage for another use.)
In a large bowl, combine the potato, carrot, celery, green pepper, onion, eggs, garlic, salt and pepper. Crumble beef over mixture; mix lightly but thoroughly.
Shape into 12 logs. Place 1 log on each cabbage leaf; overlap cut ends of leaf. Fold in sides, beginning from the cut end. Roll up completely to enclose filling. Secure with a toothpick.
Place in a greased 13x9-in. baking dish. Pour tomato sauce over roll-ups. Sprinkle with basil and parsley. Cover and bake at 350° until a thermometer reads 160° and cabbage is tender, 30-35 minutes.