Cut eggplants into 1 cm thick slices & layer them in a colander with the salt. Let them drain for 30 minutes. Wash them under cold water & dry them on paper towels. Beat together oil, lemon juice, mint, cumin, garlic & pepper. Beat together, separately, the yogurt, mint & cumin.
Heat the grill to high. Lay the eggplant slices on the hot rack & brush them with half the lemon mixture. Grill them until they begin to brown. This will take about 2 minutes. Turn over, brush with the rest of the lemon mixture & brown.
Serve grilled eggplants hot with the sauce separately as an appetizer. Or place the eggplant on a large platter & spoon the sauce over the top & serve as a vegetable accompaniment for middle eastern dishes.