Cut the eggplant lengthwise into ¼-inch-thick slices. Lay the slices on paper towels, sprinkle with the coarse salt, and set aside for 1 hour.
Preheat the broiler.
Shake or wipe any excess liquid off the eggplant slices. Brush them lightly on both sides with some of the olive oil. Place the eggplant on a broiler rack or baking sheet lined with aluminu