In a bowl, combine chicken broth, sugar, vinegar, soy sauce, salt and pepper; set aside. Peel eggplant and cut in strips about 2 inches long and 1/2 inch thick. (Do not peel if using oriental eggplant. I don't peel American eggplant either!)
Heat a wok or wide frying pan over medium-high heat. When pan is hot, add 3 tbsp oil. When oil is hot, add eggplant and stir fry for 3 minutes. Eggplant will soak up the oil immediately; stir continuously to prevent burning. Remove eggplant from pan.
Heat the remaining 2 tbsp oil in pan. Add chicken, onion, ginger, garlic, and hot bean sauce. Stir fry until meat is no longer pink, about 2 minutes.
Return eggplant to pan, pour in chicken broth mixture, cover and cook over medium-low heat until eggplant is tender, about 6 minutes. Blend cornstarch and water, and pour mixture into pan and cook, stirring until sauce bubbles and thickens. Stir in sesame oil if using, just before serving.
Serve over white rice.
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