Combine the pork with the soy sauce and allow to stand while you prepare the green beans and eggplant.
Heat a large nonstick skillet or wok over high heat and, when hot, add 1/4 cup of the vegetable oil. When the oil is hot, add the green beans (careful - this will splatter!) and stir-fry until the green beans are slightly wrinkled, 5 to 6 minutes. Using a slotted spoon, remove the green beans and transfer to paper-lined plate to drain. Add the remaining oil to the pan and add the eggplants and cook, stirring occasionally, until eggplants are lightly browned on all sides, 4 to 5 minutes. Remove the eggplant to a shallow bowl and set aside.
Add the garlic and basil to the skillet and cook for 10 to 15 seconds. Add the pork and cook, stirring, until it changes color, 1 to 2 minutes. Return the eggplants to the skillet and add the chicken stock, hoisin, dark soy, black vinegar, chili garlic sauce and sesame oil and stir to mix well. Reduce the heat to medium, cover, and cook until the eggplants are tender, 8 to 10 minutes. Return the green beans to the pan along with the cornstarch mixture and bring mixture up to a boil. When the sauce has thickened, serve immediately.