This is very different from the sweet-and-sour chicken dish often served at Chinese restaurants. It’s light and nutritious!
Pour a few tablespoons of sesame oil (olive oil is a good substitute if you have a sesame allergy) into a large skillet and turn the stovetop heat to medium. Cut 1.5 pounds of chicken breast meat into small pieces, each about twice the size of a bite. Add the chicken to the skillet and pre-heat the oven to 350 degrees.
As the chicken is cooking, slice one small cabbage head very finely. After you have verified that the chicken pieces are cooked through, add the cabbage to the skillet and stir it all together. Add more sesame oil if it is getting too dry, and turn the heat to medium-low.
As the cabbage-chicken mixture cooks, use a wire whisk to mix together (in a large bowl) a good shake of sesame oil, a good shake of balsamic vinegar, a dash of salt, a dash of pepper, and one tablespoon of honey. When this sauce is well combined, turn off the stove heat and scrape the cabbage-chicken mixture into the large bowl. Toss the cabbage and chicken with the sauce until the sauce completely coats the chicken and cabbage. Then pour the contents of the bowl into a large Pyrex dish.
Place the Pyrex dish in the oven remove it when the contents have been heated through. Serve while hot. This dish reheats nicely.