Preheat oven to 425f and set one rack to the middle and the other to the second highest level.
Cut the eggplant in half lengthwise and score the inside of the flesh with a sharp knife in a crosshatch pattern, being careful to not go through the skin. Coat the inside and outside of the eggplant with vegetable oil. Place the eggplant pieces cut side down on a parchment paper lined baking sheet. Bake on the middle level for 25-30 minutes or until a knife easily slides through all parts of the eggplant.
While the eggplant is cooking whisk together miso paste, sugar, mirin, and sesame oil.
Remove the eggplant from the oven and turn on the broiler. Discard the parchment paper and flip over each piece of eggplant so that the flesh side is facing up. Brush the miso paste, dividing evenly, into the scored areas of the eggplant.
Broil for 2-3 minutes on the higher rack. Keep an eye on the eggplant and watch for burning. It should get nicely caramelized. Remove from oven and sprinkle the sesame seeds and green onions on top. Enjoy!
