Wash the eggplant and cut it into thick diagonal slabs, cutting almost through but leaving the bottom connected so each piece opens like a book. Dust the inner cut surfaces lightly with dry cornstarch.
Finely chop the oyster mushrooms. Mash the soft tofu with a fork until creamy, then add the mushrooms, edamame, salt, white pepper, sugar, five-spice and cornstarch. Mix until combined.
Press a spoonful of filling into each eggplant cut. Heat oil in a non-stick skillet over medium-low heat and place filled pieces filling-side down first. Cook gently until golden, then flip to brown each side until tender, about 8-10 minutes.
Stir together vegan oyster sauce, soy sauce, white pepper, sugar, salt and water in a small bowl. Add a little cornstarch slurry to thicken to a glossy, pourable sauce.
Pour the sauce over the warm stuffed eggplant and let it bubble briefly. Garnish with white sesame seeds and serve hot with steamed rice.