Cut turkey into 1-inch pieces. Set aside. In a 3 1/2- or 4-quart slow cooker place mushrooms, bok choy, carrots, and onion. Add turkey. Combine in a medium bowl chicken broth, soy sauce, sesame oil (if desired), ginger, and garlic. Pour over mixture in cooker.
Cover and cook on low-heat setting for 8 to 10 hours or on high-heat setting for 4 to 5 hours. Turn off cooker. Stir in rice. Cover and let stand for 5 to 10 minutes or until rice is tender.