1.Set oven rack to center of oven, about 7 inches from element. Preheat oven to 425 degrees.
2.In a small bowl, mix sugar and miso until sugar is dissolved. Add mirin then gradually add sake until fully incorporated.
3.Cut off the stem of the eggplant then slice in half lengthwise. With a knife score the eggplant diagonally about 1/8-inch deep then score again in a crisscross pattern.
Repeat with the rest of the eggplant.
4.Soak the eggplant in water for 10 minutes, make sure eggplants are fully submerged. Meanwhile line a baking sheet with parchment. After 10 minutes dry eggplants and place cut side up on the baking sheet.
5.Brush the eggplant flesh with sesame oil then flip skin-side up. Bake eggplant for 15 minutes. Take the eggplant out and turn on the broiler.
6.Turn the eggplants over and brush the tops with miso mixture. Place eggplants under broiler for 3-5 minutes until the glaze starts to bubble. Take eggplants out and sprinkle with sesame seeds and green onions. Serve immediately.