Place the eggplant slices in a colander and toss with the salt. Let stand for 30 minutes. Rinse the eggplant well, under cold running water, and pat dry with a kitchen towel. In a small bowl, combine the garlic and vinegar and let stand while you cook the eggplant. Divide the oil between 2 large skillets and heat until it sizzles. Add eggplant slices to both skillets, without overcrowding, and fry until a deep golden on both sides, 12 to 15 minutes. Repeat with any remaining slices. Transfer the fried slices to a large bowl, without draining. Let cool. Place the cooled eggplant slices in a serving dish in layers, sprinkling each layer with vinegar-garlic mixture, pepper, salt (if needed), and cilantro. Cover and refrigerate for at least 2 hours before serving.