Nasu no Dengaku is traditionally made by broiling slender Japanese eggplants, spreading them with a sweet miso glaze, then broiling them again until the glaze is caramelized and sizzling. It's an extraordinarily simple but extraordinarily tasty dish that is probably my favorite appetizer at a Japanese restaurant.
Now, broiling is all well and good, and I've even had excellent deep-fried-then-broiled versions of the dish, but with my grill in almost constant use, I decided to up my eggplant game by grilling the sucker first before. Deep, rich miso is a natural partner for the smoky flavor of the grill. The combination rears its head all the time in Japanese cuisine (think, for example, miso soup made with miso and a broth of smoked bonito).
I start by splitting the eggplants in half lengthwise and grilling them over charcoal until nice hash marks appear but they still retain an un-cooked core—they're going to continue to cook under the broiler.
I tried finishing them 100% on the grill by spreading them with the miso glaze (a mixture of miso, sake, and mirin), transferring them to the cooler side, and covering them with a lid, but the miso glaze never got quite the level of caramelization and crustiness I was after. Tasty, to be sure, but not ideal.
Instead, I prefer to transfer the grilled, miso-spread eggplant halves to a broiler-safe pan and finish them off in the oven. If you've got other things to cook, like, say, these awesome beef and scallion rolls (negimaki), you can pull off the eggplant, get'em in the broiler pan, and hold them until you're ready to eat. Then it's just a few minutes under a hot broiler to crisp up, and you're good to go.
A shower of scallions and toasted sesame seeds are entirely unnecessary, but look pretty and taste nice, so on they go.