Heat 2 tablespoons of oil in a large skillet or wok over medium-high heat until almost smoking. Cook and stir the eggplant cubes until they begin to brown, 3 to 5 minutes. Remove the eggplant with a slotted spoon, and set aside.
Heat 2 more tablespoons of oil in the skillet over medium-high heat, and cook and stir the onions just until they begin to soften, about 30 seconds. Stir in the garlic, and cook and stir an additional 30 seconds. Mix in the soy sauce, water, oyster sauce, chili garlic sauce, sugar, and black pepper, and stir to form a smooth sauce. Return the eggplant to the skillet, lower the heat, and allow the vegetables and sauce to simmer until the eggplant is tender and almost all the liquid has been absorbed, about 5 minutes. Drizzle sesame oil over the dish, and give one final brief stir to combine.