In a small bowl, combine the tamari, hoisin, mirin and water. Set aside.
Spread the oil in the bottom of a 5.5-6 quart slow cooker and turn on High. Add the garlic and ginger and arrange the baby bok choy on top. Sprinkle with the scallions and pour the tamari mixture over all. Change the heat setting to Low, cover and cook for four hours, or until the bok choy is tender. Serve hot.