You put hot coals in the center and cover with foil. I don't know how the eggplant is prepared before that. Thanks!
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I don't think I've ever heard of putting coals directly into the eggplant. I know you can grill eggplant whole directly on glowing coals or above them (prick with a fork several times and turn regularly until soft) and remove the charred skin afterwards. You get a nice smoky flavor.
Please do let us know if you experiment some with the technique you are asking about, it sounds very interesting.
I've never heard of smoke and mirrors eggplant, but I see that you've tagged the question with the term "Indian"--are you talking about Baingan Bhurtha? The way we prepare the eggplant at home is by baking it (350° for 45 min, make sure to put some foil underneath to catch the juices), letting it cool, then peel the skin away and mash/chop the insides before adding it to the spices mix. Combining roasted eggplant and heavy, smoky, and punchy flavors like cumin, garam masala, gound coriander seeds, and peppers gives the dish a huge kick. Hope it helps, or at least gives you an alternate option to using eggplant!