Combine the first six ingredients in a small bowl, beating with a wire whisk until blended. Set aside.
Brush both sides of eggplant slices with the 3 tbsp olive oil. Arrange eggplant slices in a single layer ona n ungreased baking sheet. Sprinkle with 1/4 tsp salt and 1/4 tsp pepper. Broil 5 1/2 inches from heat (with electric oven door partially opened) for 5 minutes on each side or until tender and lightly browned. (Smaller eggplants will need less time).
Arrange eggplant slices on an ovenproof platter or casserole dish, overlapping slices slightly. Arange cheese slices over the eggplant slices. Broil for 1 minute or until cheese melts.
Whisk the reserved olive oil mixture until blended. Spoon over the eggplant. Garnish with fresh basil sprigs if desired.