Whisk the marinade ingredients together and let stand 10 minutes.
Preheat an outdoor grill to medium. Slice the eggplant 1/2 inch thick, salt and let stand in a colander 20 minutes. Rinse briefly and pat dry.
Pour the marinade over and let stand at least 10 minutes or up to overnight in the refrigerator.
Grill, reserving the marinade, until cooked through and lightly browned, 10 to 15 minutes. Serve with the reserved marinade and a sprinkle of sesame seeds.