Preheat the broiler to medium. Halve 2 long Japanese eggplants lengthwise and score the cut flesh in a crisscross pattern without piercing the skin.
Place cut-side up on a rack over a metal baking sheet. Broil for 5 minutes, then turn and broil the skin side for 5 minutes.
Meanwhile, stir 2 tablespoons of yellow miso, 2 tablespoons of sake, ½ tablespoon of toasted sesame oil, ½ tablespoon of light brown sugar, and 1 teaspoon of mirin in a small saucepan.
Bring to a gentle boil over medium heat, stirring. Lower the heat and simmer for a few minutes, until glossy.
Turn the eggplant cut-side up. A skewer should slide easily into the thickest part; broil longer if still firm.
Brush the hot flesh with the miso sauce. Broil for a few minutes until lightly charred, watching closely. Sprinkle with toasted sesame seeds and shredded shiso.
