Slice the eggplants in half lengthwise.
Make 4 to 5 slits crossways in the cut side.
Salt the eggplant flesh and stand the halves in a colander to drain for 30 minutes.
Rinse the halves, squeeze out the moisture, and pat them dry.
Brush the oil well into the slits and over the surface of the eggplant.
Prick the peel on the rounded side of the eggplant with a fork.
Grill on an oiled rack about 5 inches from the coals, cut side down, until brown, about 4 minutes.
Turn the eggplant halves, move them to the side of the grill, and cook on the rounded side 4 to 6 more minutes, until tender, brushing the cut side with additional oil.
Alternatively, the eggplant can be broiled 4 to 5 inches from the broiler flame for 8 minutes.
No need to turn the eggplant when using a broiler.
Brush the cut side with oil again just before serving.