Preheat your broiler (or prepare a hot grill). Trim and halve the Japanese Eggplant lengthwise and score the flesh in a crisscross pattern, taking care not to cut through the skin.
Brush the cut surfaces with Neutral Oil and place the eggplant, cut-side down, on a baking sheet or grill rack. Broil/grill until the skin blisters and the flesh is very soft, about 8–12 minutes depending on size.
While the eggplant cooks, make the miso glaze: combine 3 tbsp Miso, 1 tbsp Mirin, 1 tbsp Sake and 1–2 tsp Sugar in a small saucepan. Warm gently over low heat, stirring, until the mixture is smooth and slightly thickened (about 2–4 minutes). Remove from heat.
Turn the broiled eggplant flesh-side up and spoon or brush a generous layer of the warm miso glaze over each half.
Return the glazed eggplant to the broiler (or grill) and broil for 1–3 minutes, watching closely, until the glaze is bubbling and lightly caramelized—do not burn.
Remove from the oven and sprinkle with toasted White Sesame Seeds and thinly sliced Scallion before serving. Serve hot or warm.
