Slice the chicken into thin pieces, 1/8-inch thick and 2 to 3 inches long.
Heat the oil in a large skillet or wok over medium heat. Add the chicken and cook for 4 to 5 minutes, tossing over high heat until it begins to brown evenly. Add mushrooms and carrots and stir fry briefly, shaking the pan and tossing the chicken and mushrooms together.
Add the cabbage and stir to combine well. Add the fish sauce and sesame oil. Cook the cabbage briefly before adding the chicken broth. Bring quickly to the boil and reduce for a moment before adding the honey, vinegar, salt and pepper. Toss for another 1 minute. Add the dissolved cornstarch and stir in to coat evenly. Remove from the head before the cabbage loses its crispness and color and serve.