Preheat your grill or broiler on medium. While you wait, wash 2 eggplants and dry with kitchen paper. Remove the stems and cut them in half lengthways, then score the flesh with a crosshatch pattern.
If using globe eggplants (or particularly thick ones), cut into 2-3cm rounds instead and score on one side.
Once the grill is fully preheated, place the eggplant halves on a wire with the flesh side facing the heat source and grill for 5 minutes.
While the eggplant cooks, combine the sauce ingredients (2 tbsp yellow miso paste (awase), 2 tbsp sake, ½ tbsp toasted sesame oil, ½ tbsp light brown sugar and 1 tsp mirin) in a small saucepan and bring to a gentle boil over medium heat while stirring continuously. Reduce the heat to low and simmer for a few minutes, stirring occasionally to prevent burning.
After 5 minutes, flip the eggplant and grill the skin side for another 5 minutes.
Flip the eggplant pieces once more and test the doneness by piercing the thickest part with a chopstick. If it's still firm, grill for another 2-3 minutes. Once softened, brush the scored side with the miso sauce and grill for a few minutes until the miso glaze chars lightly on top.
Transfer to serving plates, then sprinkle with toasted white sesame seeds and shredded perilla leaves (shiso). Enjoy!
Notes
Taste your miso first: Awase tubs run 5 to 13 percent salt with no label warning. Sharp on the fingertip, pull the miso back by a teaspoon and push the sugar up.Press the flesh before glazing: If a chopstick meets any resistance, keep grilling. Glazing too early is how this dish fails most often. Color is not a doneness signal.Glaze a hot eggplant, not a cooled one: A cooled cut face will not grip the paste. Brush before the eggplant rests off the first heat.