1. Preheat broiler.
2. Hollow out top and bottom halves of bread, leaving a 1/2-inch-thick shell. Place torn bread in a large bowl. Add milk, stirring with a fork until smooth. Add oregano, salt, turkey, and egg white to bread mixture, stirring just until combined. Working with damp hands, shape turkey mixture into 12 meatballs.
3. Heat a large nonstick skillet over medium heat. Add 1 tablespoon oil to pan; swirl to coat. Add meatballs; cook 5 minutes, turning to brown on all sides. Remove meatballs from pan. Add remaining 1 teaspoon oil to pan; swirl to coat. Add onion and garlic to pan; sauté 4 minutes or until tender. Add wine; cook 1 minute, scraping pan to loosen browned bits. Stir in marinara, basil, and vinegar; bring to a boil. Return meatballs to pan. Cover, reduce heat, and simmer 15 minutes or until meatballs are done.
4. Arrange rolls, cut sides up, on a baking sheet; broil 1 minute or until toasted. Top bottom half of each roll with 3 meatballs, about 1/3 cup sauce, and top half of roll. Sprinkle evenly with Parmigiano-Reggiano.