Yakinasu (grilled eggplant) is one of those incredibly simple but irresistible dishes... I can't help but order it whenever I see it on an izakaya menu. Sometimes we've even bought it at department stores to take home, as when Hiromi and I ate at her parents' home during my last trip to Japan.
Ideally grilled over Japanese charcoal with a shichirin, yakinasu can also be prepared on an ordinary grill or with a small flame on a gas konro. I used to rely on the broiler feature of my stove, but that requires very careful monitoring to pull off successfully.
You can use either the long, skinny 5-6" nasubi (Japanese eggplant) for this, or the 2-3" roundish ones reminiscent of kyō-nasu (Kyoto eggplant), sometimes called Indian eggplant here in the U.S. The larger European-style eggplants common in the U.S. are probably too big for this.
The one important question to ask when preparing this: Skin on or skin off? I tend to prefer the variations which keep the skin, mostly because it looks more appealing, but you can get a slightly smokier flavor if you're willing to sacrifice it. If you do that, you grill or broil the eggplant on all sides until the skin is more or less blackened, then wrap up the eggplant in aluminum foil, or place it in an airtight container to steam the skin until it becomes easy to remove.
When you remove the skin, you might dress the eggplant with some katsuobushi and soy sauce, or some nerimiso (sweetened miso sauce). Since I'm vegetarian, I make the latter.
For the skin-on version, I typically score the skin on either side, first lengthwise, then about 30 degrees off axis. I've chosen to cut the eggplants in half before grilling, and I rubbed the flesh with a little salt. Each side is grilled gently until the flesh slightly softens. After a few minutes of rest, the eggplant becomes a bit more tender thanks to residual heat, so it's better not to overcook it.
This version is ideal with some freshly-grated ginger, chopped scallions and a little splash of Japanese soy sauce.