For glaze, stir all ingredients together and chill until ready to use.
Preheat a grill on high heat. Slice eggplant on the bias into pieces 1/2-inch thick. Grill until soft and showing grill marks, about 3 minutes, then turn over. Brush glaze on cooked side of eggplant, then turn over to cook 1 minute while glazing second side. Remove from grill and set aside on a platter. Repeat same method with scallops.
Serve eggplant and scallops warm and garnished with sesame seeds.
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