In a small mixing bowl, combine the soy sauce, chicken broth/stock, rice wine vinegar, chili paste, cornstarch, and 1 tbsp of sesame oil. Mix well and then set aside.
Heat the remaining 1 tbsp sesame oil in a large saute pan over medium-high heat.
Add the chicken and onion and cook until the chicken is well-browned and the onion is tender, about 6-8 minutes.
Add the eggplant and cook until eggplant is mostly tender but not yet cooked through, about 3-4 minutes. Add the garlic and green onions, and cook for 1 minute, until the garlic is fragrant.
Add the prepared soy sauce mixture to the pan, cover, and cook for 5-6 minutes, or until the eggplant is tender and the sauce is thickened.