I love these cut longways in 3-4 inch strips with a some soy sauce (I use low-sodium), garlic, and a little ginger. I add chopped green onion at the end (optional).
I cut them into chunks and simmer them with a mixture of white miso, sake, sugar and sesame paste (tahini) - or even peanut butter - and a little soy sauce (not too much, or it will overpower the mix). This is such a simple preparation I don't even have a recipe, just add stuff to taste. Simmer the whole mixture until the eggplant chunks are tender. If the eggplants are small enough, leave the peels on, otherwise peel them first.
This is a complicated one, and a bit on the heavy and rich side, but it's good when you have the time and feel like splurging a bit.
Cut eggplant into 1 inch segamant, then slice a pocket into each, not cutting all the way through.
Mix together some ground pork, chopped dried shrimp, minced garlic, minced ginger, soy sauce, saseame oil, rice wine vinegar, a bit of sugar and some hot chili oil.
Stuff eggplant with some meat mixture.
Coat each eggplant piece with a quick tempura batter and fry and set aside.
Stir fry together a sweet and sour sauce with garlic, ginger, soy, sugar, black vinegar and a bit stock, thicken with cornstarch slurry.
Add all the fried eggplant pieces to rewarm and coat with sauce.
This is called Fish Flavor Eggplant, a pretty well known Chinese eggplant dish, although my 'recipe' isn't exact, it's more of a 'method'.
Slice once lengthwise, drizzle with olive oil, sprinkle with S&P, and put on a hot grill. Turn after a couple of minutes, then take 'em off. Eat as they are, or with shoyu, or mashed with some fermented bean paste.
The last time I did this, I also grilled some bell peppers and red onions, cut everything into bite-sized pieces, and tossed them together. I had intended to dress w/ balsamic vinegar, but it tasted so good without that I just left it as it was.