If you're using whole-milk plain yogurt instead of _lebneh_, you'll have to allow extra time (at least 8 hours) for draining.
Active time: 20 min Start to finish: 50 min
Brush eggplant slices generously with oil on both sides and sprinkle with remaining 3/4 teaspoon salt. Grill slices on lightly oiled grill rack, covered only if using a gas grill, turning over occasionally, until eggplant is tender, 12 to 15 minutes total. Transfer as cooked to a platter, arranging slices in 1 layer. Put a spoonful of yogurt mixture on each eggplant slice and top with a mint leaf.