I found this recipe on-line from Food and Wine. The recipe is by Chef Cara Stadler.
I am looking for good vegetarian recipes and this is superb!

The original recipe called for "shiso" which I could not find at the Asian market.
Evidently it is a kind of mint and I decided to substitute cilantro and it worked just fine.

The instructions said to turn the sugar to caramel which I did not do but I did dissolve it in the water on the stove.
I will give the instuctions as written and do as you wish.

DRESSING:
1 Tbsp. SUGAR
6 Tbsp. BLACK VINEGAR
6 Tbsp. CANOLA OIL
1 Tbsp. SOY SAUCE

EGGPLANTS:
3 Tbsp. SHIRO (WHITE) MISO
1 1/2 Tbsp. MIRIN
6 Tbsp. CANOLA OIL
1 pound JAPANESE EGGPLANTS (the long purple ones) halved lengthwise

SALAD:
Several of the small HEIRLOOM TOMATOES, cut in half-inch dice
1/2 pint CHERRY TOMATOES, halved
1/3 c. DILL, chopped
1/4 c. CILANTRO (or shiso, if you can find it), chopped
1 Tbsp. SCALLIONS, minced

MAKE THE DRESSING: Preheat the oven to 350°.
In a small pan, combine the sugar with 1 tsp. water. Cook over low heat, swirling the pan until the sugar melts and an amber caramel forms... about 4 minutes.
Whisk in the black vinegar. Remove from the heat and let cool to room temperature.
Whisk in the oil and soy sauce.

PREPARE THE EGGPLANTS: In a bowl, mix the miso with the mirin.
In a nonstick skillet, heat 3 Tbsp. of the oil.
Add half the eggplant cut side down and cook over moderate heat until deep golden, 3 minutes.
Repeat with remaining eggplant.
Transfer the eggplant cut side up to a baking sheet.

Spread the miso mixture on the cut sides of the eggplants.
Roast for 15 minutes until the eggplants are very tender.
Transfer to a platter.

MEANWHILE, MAKE THE SALAD: In a large bowl, toss the tomatoes with the dill, cilantro and scallions.
Toss with 2/3 of the dressing.

Spoon the salad over the warm eggplants and drizzle with the remaining dressing.
Garnish with additional dill and cilantro, if desired and serve.

I served this with steamed buns that I had bought frozen from the Asian market.