Mix onion slices and 4 cups ice water in a large bowl; let stand 30 minutes. Drain and pat dry with paper towels.
Whisk together vinegar, olive oil, 2 tbls. water, sugar, salt, pepper and garlic. Stir in basil and parsley.
Layer half of the tomato slices in a shallow dish. Top with half of the onion slices. Drizzle with half of the dressing. Repeat with remaining tomato slices, onion slices and dressing. Cover and refrigerate 30 minutes.
Sprinkle with Parmesan curls, if using, and serve with French bread. Serve at room temperature.