Position an oven rack in the upper part of the oven and preheat the broiler. Line a pan with foil.
Whisk the miso and soy sauce together in a small bowl. Trim the eggplant stems and halve lengthwise. Lightly score a diamond-like pattern into the flesh of the eggplant. Put the eggplants, skin-side up on the prepared pan.
Broil the eggplants until the skin discolors, about 1 minute. Turn the eggplants over, lightly brush the top with oil, and broil until softened, about 4 minutes. Brush each eggplant half with the miso mixture and broil until the top is bubbling, about 1 minute. Serve.