Notes: If making up to 2 days ahead, cover and chill. Bring to room temperature to serve.
1. Rinse eggplant and peppers; pat dry. Trim and discard eggplant stem; cut eggplant crosswise into 1/2-inch-thick slices. Peel onion and cut crosswise into 1/2-inch-thick slices. Brush eggplant slices, peppers, and onion slices with about 2 tablespoons olive oil total.
2. Lay vegetables in a single layer on a barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid on gas grill. Cook, turning as needed to char all sides, 8 to 12 minutes total. Transfer to a bowl; let stand until cool, about 15 minutes.
3. Meanwhile, in a small bowl, mix 1/4 cup olive oil, vinegar, basil, and garlic.
4. Peel, stem, and seed peppers. Quarter lengthwise.
5. In a deep dish (at least 4-cup capacity), layer vegetables with herb marinade (using all the marinade) and salt and pepper to taste. Cover and let stand 30 minutes to 4 hours, or cover and chill up to 2 days.