1, Trim the stem end of each eggplant, peel, and slice lengthwise into 1-inch slices. Sprinkle with salt and set aside to drain, 1 hour. After an hour, pat slices dry with a paper towel.
2, While the eggplant slices are draining, prepare a medium fire for direct-heat grilling in a charcoal grill (you should be able to hold your hand 1 inch above the grate for only 4 to 5 seconds).
3, When the coals are ready, drizzle the leeks with 2 tablespoons of the oil and sprinkle with salt and pepper. Place the leeks on the grate and cook, turning as needed, for about 15 minutes, until soft and charred in spots. Transfer to a plate, cover with plastic wrap, and let steam while you cook the eggplant.
4, Drizzle the eggplant slices on both sides with the remaining 2 tablespoons oil, then sprinkle on both sides with salt and pepper. Grill the slices, turning occasionally, for about 20 minutes, until very soft and browned.
5, Remove the eggplant slices from the grill. When cool enough to handle, cut into ½-inch cubes and transfer to a serving bowl. Cut the leeks crosswise into 1-inch-thick slices and add to the eggplant. Add the cilantro and toss to combine.
6, In a small bowl, whisk together the spicy soy sauce and lime juice. Pour over the eggplant-leek mixture and toss to coat evenly. Season with additional salt and pepper and serve.