Preheat the broiler.
In a small bowl, whisk together the miso, rice vinegar, water, sugar, and ginger until the sugar has dissolved.
Lightly grease a baking sheet, and arrange the eggplant on it cut side up. Brush the eggplant tops with vegetable oil. Broil the eggplant 4-6 inches from the heat source for 4-5 minutes, until it turns pale golden and begins to soften. Remove pan from broiler and generously brush with the miso mixture. Broil for 2 more minutes, then brush the eggplant with miso again, and broil for 2 more minutes. Brush the eggplant with the miso again, and rotate the baking sheet 180˚, and broil again for 2-3 minutes until the eggplant is tender and golden-brown.
Serve immediately, sprinkled with the chopped scallions.