Place eggplant on several layers of paper towels; sprinkle salt over cut sides of eggplant. Let stand 15 minutes; blot dry with paper towels.
Combine rice vinegar and next 5 ingredients; stir well. Brush over eggplant; let stand 10 minutes. Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place eggplant on rack; grill, uncovered, 5 minutes on each side, basting often with remaining sesame seed mixture.