They're not usually smoked - not the way we think of 'smoked' - they're roasted whole. They develop a smoky sort of character this way because the skin is charred.
I grill-roast instead and use good lump. This adds a more distinctive flavor. If the place you had it does this or something similar so much the better.
1 purple eggplant, about 2 lbs
1 med onion, minced
1/4 c evoo, plus more to finish
1 small green bell pepper, finely chopped
1 clove garlic, minced
2 large tomatoes, peeled, seeded, finely chopped (fresh recommended - but you can use canned, diced if necessary; 1 can, drained)
1/2 tsp sugar
1.5 tsp salt
freshly ground white pepper (or use black)
1 lemon, halved
2 tbls minced fresh parsley*
Set your grill up for indirect cooking (coals banked well to both sides), using lump, or use your WSM. (You could also try charcoal with a little wood.) Temps of 400-425 need to be achieved so plan accordingly and get your cooker going. Lightly oil the grate and put on the eggplant. Roast, turning two or three times, till the eggplant is very soft and the skin is charred, 1-1.25 hours, more or less, depending on temps. Remove the eggplant to a plate and allow to cool a bit.
Meanwhile, heat the 1/4 c oil in a med sauté pan then sauté the onion till just soft, 4-5 min. Add the bell pepper, stir in, and cook another 3-4 min. Add the garlic and, stirring constantly, cook till very fragrant and well combined, 1-2 min more. Remove the contents of the pan to a large bowl and rinse and dry the pan.
Remove the skin from the cooled eggplant, scraping off and reserving any flesh that clings to it; discard the skin. Very finely chop the eggplant and add to the onion/pepper/garlic in the bowl. Add the tomatoes, sugar, salt, and a turn or two of the white peppermill. Mix well.
Heat a little evoo in your pan then add the contents of the bowl. Bring just to a strong simmer, stirring frequently, then partially cover, lower the heat to low, and cook 45 min, stirring occasionally. Remove the lid and continue cooking, stirring occasionally, till the excess moisture has evaporated and the mixture is thickened.
Remove from the heat and stir in the parsley and the juice from half a lemon. Adjust salt and pepper and allow to cool. Taste again and add more lemon if desired. Remove to a bowl and chill well.
* Though cilantro is not standard, so what? If you think the salad you're seeking has it and/or you want to try it feel free.