Place the prepared chicken and vegetables (except the scallions) in the slow cooker. Add all the sauce ingredients (except the sesame oil and seeds). Stir well to coat the chicken and vegetables evenly.
Turn the slow cooker on high heat. Cover, and cook for about 4 hours. (You can cook on low heat if you’ll be out longer, about 6 hours). Stir in the scallions, sesame oil and sesame seeds. Skim off excess fat before serving, if desired. Serve with a bowl of rice.
Stove top method: To make this dish on the stove, add 1-1/2 cups water to a large pot along with the chicken and the sauce (except the sesame oil and sesame seeds). Stir well. Bring it to a boil over high heat. Reduce the heat to medium and cook, covered, for 15 minutes, stirring occasionally. Stir in the vegetables (except the scallions). Cover, and cook for an additional 15 minutes, stirring occasionally. Continue to cook, uncovered this time, until the chicken is tender and the sauce is slightly thickened, about 10 minutes. Stir in the scallions, sesame oil and sesame seeds right before turning off the heat.