In a small bowl, mix together the vegetable broth, soy sauce, vinegar, brown sugar, chili oil, and red pepper flakes. Set aside.
Place a wok over high heat until a drop of water sizzles on contact. Add the peanut oil and swirl to coat the wok.
Add the eggplants to the wok, and stir-fry for 2 to 3 minutes, until the outsides become golden brown. Turn down the heat to medium-high, and add the scallions, ginger, and garlic. Stir-fry for about 30 seconds, and then add the broth mixture; toss the vegetables for 2 to 3 minutes until they are coated with the sauce. Simmer the vegetables for 2 to 3 minutes, allowing the eggplant to absorb the sauce.
