Trim the ends of the eggplants and cut on a sharp diagonal into 2-inch batons about 1/2 inch thick. Toss with the cornstarch until every piece is lightly and evenly coated.
Heat 2 tablespoons of oil in a large wok or heavy skillet over high heat until shimmering. Add half the eggplant in a single layer and sear undisturbed for 2 minutes, then turn and cook 4-5 minutes total until golden on two or three sides and softening. Transfer to a plate and repeat with more oil and the remaining eggplant.
Lower the heat to medium-high. Add a drizzle of oil if the pan looks dry, then stir-fry the garlic, ginger, and chiles for 30 seconds to 1 minute, until fragrant and the garlic is just pale gold.
Stir in the light soy sauce, dark soy sauce, and sugar; cook 30 seconds, stirring, until the sugar dissolves and the mixture bubbles.
Return all the eggplant to the pan and toss to coat. Add 1/4 cup water, cover, and cook 3-4 minutes, until the eggplant is completely tender and the sauce has thickened to a glossy glaze.
Uncover, stir in the black vinegar and scallions, and toss for 30 seconds. Drizzle with sesame oil, taste for salt, and serve immediately over steamed rice.