How to Make It
Preheat the oven to 350°. Using a small sharp knife, make 1/4-inch-deep crisscrossed slashes in the center of the fleshy part of each slice of eggplant; take care not to cut through the skin so the slices remain intact. Lightly brush the eggplant with oil and season with salt and black pepper.
In a large skillet, heat 1 tablespoon of the oil. Add the eggplant slices in batches and cook over moderately high heat until golden brown, about 4 minutes per side; add more oil as needed. Transfer the eggplant to a large rimmed baking sheet and bake for about 20 minutes or until meltingly tender. Remove from the oven. Preheat the broiler.
While the eggplant roasts, combine the sake, mirin, sugar, miso and cayenne in a small saucepan and cook over moderately high heat until reduced by half, about 15 minutes.
Generously brush both sides of the eggplant slices with the sake-miso glaze. Broil for about 1 minute per side, shifting the pan for even browning; the slices should be sizzling and caramelized. Serve hot or at room temperature.