To prepare: Use a vegetable peeler to peel lengthwise strips of skin from the eggplant: it will look striped. Alternatively, use a fork to score the skin deeply. (Cooked eggplant skin can be tough; smaller eggplant can have more tender skin, so you can leave it all on if you prefer.)
Trim the ends. Cut the eggplant crosswise into rounds about 3/8 inch thick. Brush both sides of the slices with plenty of olive oil and season well with kosher salt just before grilling.
To grill: Heat a gas grill to high, put the eggplant slices on the grate, and cover the grill. Grill, checking occasionally with tongs, until the slices are well browned on both sides, 3 to 4 minutes per side.
Move the slices from the heat and stack them to finish cooking (put them on an upper rack, set them over a turned-off burner, or wrap them in foil off the grill). Let sit 15 to 20 minutes. (Eggplant will often still be raw in the middle without this last step of letting the residual heat steam the flesh.)