2Put the peanut oil in a large skillet, preferably nonstick, over medium heat. About 2 minutes later, add the eggplant, skin side down. Cook until nicely browned, adjusting the heat and rotating the pieces so they brown evenly, about 10 minutes. Turn and cook on the flesh side until brown, then continue to cook, turning as necessary, until tender, another 10 minutes or so.
3When the eggplant is almost done, combine the miso, sugar, mirin, and vinegar in a small saucepan over medium heat. Cook for about 1 minute, stirring. Remove the eggplant and spread a thin coating of the miso mixture over each half; top with the sesame seeds. Serve hot or at room temperature.