Preheat oven to 400F/200C and line a baking sheet/tray with foil.
Trim the ends off the eggplants and cut in half lengthwise. Using the tip of a sharp knife, score the flesh of the eggplant in a criss-cross pattern without cutting through to the skin (see photos). Brush the eggplants all over with oil, only very lightly on skin side, and place the eggplants skin side down (cut side up) on the lined baking sheet.
Roast the eggplant halves for around 20 - 30 minutes until the flesh is tender, and the tops only just starting to color. Remove from oven and allow to cool very slightly.
As the eggplant is cooking, mix together the glaze ingredients - miso paste, mirin, sake and sugar. Mix until you get a smooth paste - the miso may be a little lumpy at first but press any lumps with the back of a spatula/spoon to get them to mix in. If that doesn't work, gently warm the mixture to help it combine.
Once the eggplant has had a couple minutes to cool, preheat the broiler/overhead grill. Brush the cut top of the eggplants with the miso glaze, dapping some into the criss-cross cuts. Be relatively generous with the glaze, but don't have it dripping down the sides.
Place the eggplants until the broiler/grill for around 3 - 4 minutes until the tops are gently caramelized brown. Take care to watch them closely and turn as needed as they can quickly go from brown to burnt. Sprinkle with toasted sesame seeds and serve warm.