Heat the oven to 220C / 425F and line a sheet pan (33 x 46 cm / 13 x 18 inch) with parchment.
Halve the eggplants lengthwise. Score the cut side in a crosshatch pattern, cutting about halfway into the flesh without piercing the skin.
Brush the cut sides with oil and season with salt. Place the halves cut side down on the sheet pan.
Roast for 15 to 18 minutes, until the flesh is tender and a knife slides in with no resistance.
While the eggplant roasts, whisk the miso, mirin, soy sauce, brown sugar, ginger, garlic, sesame oil, and water in a small bowl until smooth.
Flip the eggplant halves cut side up. Brush generously with about half the glaze.
Switch the oven to broil on high. Broil for 3 to 4 minutes, watching closely, until the glaze bubbles and browns in spots and the edges char slightly.
Remove from the oven and brush with the remaining glaze while still warm.
Scatter with sesame seeds and sliced scallions. Serve warm over rice.