Prep: Preheat oven to 400°F (204°C). Cut the eggplant in half lengthwise, then score it - with the cut side facing up, lightly slice on a diagonal all the way along the eggplant. Slice in a diagonal direction the other way as well, making sure to only go about ½-inch deep.
Bake: Brush sesame oil evenly over the cut side of both halves, then place cut side down on a parchment-lined baking sheet. Bake for 20 minutes, or until tender.
Miso: Stir together miso paste, mirin, and sugar. When eggplant is finished cooking, carefully remove it from the oven, flip it so the cut side is facing up, and spread the miso onto it.
Broil: Set eggplant cut side up, put back in the oven (middle rack), and turn the oven to broil. Broil, watching carefully, until miso mixture is golden brown and bubbling.
Serve: Serve hot with sliced green onions, sesame seeds, and rice.