Prepare eggplants by washing them, removing stems, and cutting in half lengthwise. Set aside.
In a small saucepan, simmer apple juice, cranberry juice, and rice vinegar over medium heat for 2 minutes.
Stir in miso paste until smooth.
Add agave nectar, reduce heat to low, and stir occasionally while eggplants are broiled.
Brush cut sides of eggplant with sesame oil.
Place eggplants cut-side down in a glass baking dish and broil in oven for about 3 minutes but do not char.
Turn eggplants over and cook until tender, about 3 more minutes.
Spoon on miso sauce and broil for another minute.
Garnish with sesame seeds and green onion and serve hot.