Slice the eggplant into 1/2-inch-thick rounds. Soak in a bowl of lightly salted water, 15 to 20 minutes; drain and squeeze out the excess moisture.
Meanwhile, slice the tomatoes and zucchini into 1/2-inch-thick rounds. Stem and seed the bell pepper; slice the pepper and onion into 1/2-inch-thick rings.
Heat a grill or grill pan to medium high. Brush the vegetables with the olive oil on both sides and season with 1/2 teaspoon salt and pepper to taste. Grill the vegetables (in batches if necessary), turning, until soft and marked, about 6 minutes for the tomatoes, 7 to 8 minutes for the bell pepper, onion and zucchini, and about 10 minutes for the eggplant. Let cool.
Drizzle the vegetables with the vinegar. Divide the zucchini and eggplant among plates and arrange in a circle, overlapping slightly. Top with the bell pepper, tomato and onion. Sprinkle with the basil.