In small bowl, whisk rice wine (or mirin), soy sauce, toasted sesame oil, and brown sugar. In 6-quart slow cooker bowl, layer chicken breasts, soy mixture, garlic, and fresh ginger.
Cover bowl with lid and cook 5 to 6 hours on low, until chicken is tender. Transfer chicken to cutting board; shred and return to slow cooker bowl. Serve chicken mixture with warmed white rice and steamed broccoli florets.
Garnish with sliced green onions and red chiles.
