Preheat oven to 375 degrees Fahrenheit.
Slice the eggplant lengthwise and then create a cross-hatch pattern in the flesh, taking care not to cut through the eggplant.
Sprinkle the eggplant flesh with salt (this will remove excess moisture and make the eggplant less astringent).
Whisk together the miso, sake, mirin, and sugar in a medium mixing bowl.
Pat the eggplant dry with paper towels. Heat a large sauté pan over moderate heat and coat with neutral oil.
Make sure the oil is smoking hot (this will season the pan and prevent the eggplant from sticking to the bottom of the pan). You can determine this by adding a few drops of water to the pan; the water should dance on the surface and dissipate after a few seconds.
Allow the oil to glisten, and place the eggplant in the pan, flesh side down. Sear the eggplant (you might need to do this in two batches if they all do not fit in the pan) for 2-3 minutes until a beautiful golden brown. If you have a weight, place this on top of the eggplant to create a beautiful sear.
Remove the eggplant pieces from the pan and place them on an aluminum-lined or parchment-lined sheet tray flesh side up.
Liberally glaze the miso sauce over the flesh of the eggplant and place it in the oven.
Cook until the eggplant is tender, about 12 minutes. During this time, you can baste the eggplant again and rotate your pan in the oven.
Take the cooked eggplant out of the oven and turn your oven to a high broil.
Liberally baste your eggplant again, place the tray on the top portion of your oven, and cook for about 2 minutes until the sauce bubbles and all of your eggplant becomes golden brown (you might need to rotate your pan in the oven for this step). If you have extra sauce, it’s perfect to save to glaze fish or chicken in your fridge.
Garnish the cooked eggplant with the green onions.