Heat 1/4 cup of oil in the wok on high heat. Add the eggplant and and stir-fry until the pieces are brown and fork tender, but not mushy, about 4 minutes. Transfer the eggplant to a plate lined with paper towel and drain. Pour off the oil in the wok and wipe it clean.
Add the remaining oil to the wok with the garlic and chilies and stir-fry for about 20 seconds. Add the onion and about 3/4 of the red pepper and stir-fry for about 10 seconds. Add the eggplant and stir in the soy sauce, sugar, and water and stir-fry until the liquid is bubbling, about 1 to 2 minutes. Add the water and cornstarch mixture and stir in, then add most of the basil leaves. Stir until the sauce thickens, about 1 minute.
Transfer to a serving platter and garnish with the remaining pepper strips and basil. Serve immediately.