1. Combine oil and minced thyme, basil, and parsley.
2. Trim eggplant ends and discard. Rinse eggplant, cut into 24 equal rounds, and brush lightly with some of the herb oil.
3. Rinse and core tomatoes, then trim thin slices off tops and bottoms. Cut yellow tomatoes into 24 equal rounds; cut red tomatoes into 12 equal rounds.
4. Cut cheese into 12 equal rounds.
5. Lay tomato slices in a 10- by 15-inch pan. Drizzle with herb oil and sprinkle with salt and pepper.
6. Lightly oil a barbecue grill over a solid bed of medium-hot coals or medium-high heat on a gas grill (you can hold your hand at grill level only 3 to 4 seconds). Lay eggplant on grill; close lid on gas barbecue. Cook eggplant, turning once, until soft when pressed, 5 to 7 minutes total. Let cool.
7. For each tortino, stack 1 slice each yellow tomato, eggplant, mozzarella, and red tomato, then top with 1 more slice each eggplant and yellow tomato. Set stacks on a platter. Reserve 2 teaspoons of pan juices from tomatoes; use remainder in other salads.
8. In a 2- to 3-quart pan over high heat, boil vinegar until reduced to 2 tablespoons, 5 to 7 minutes, stirring as it nears the end of cooking.
9. Mix the reserved tomato juices with vinegar and drizzle over tortinos. Garnish with thyme sprigs.