Peel ginger and cut into matchsticks 1/8 to 1/4 inch thick and 2 to 3 inches long (you should have 1 1/3 cups).
Rinse ribs, drain, and lay in a single layer in a 12- by 16-inch casserole at least 2 inches deep (5 to 6 qt.). Evenly distribute ginger, onions, and pineapple over and around meat. Mix 1 cup water with 1/3 cup soy sauce and add to casserole. Cover tightly with foil.
Bake in a 375° oven until meat is very tender when pierced, 2 3/4 to 3 hours; halfway through baking, turn ribs in sauce and, if necessary, add water to bring liquid level up to 3/4 inch.
Uncover ribs and bake until browned, about 10 minutes. Skim fat from juices and discard. Scatter sliced mint over meat; garnish with mint sprigs. Add soy sauce to taste.