5 tablespoons balsamic vinegar, divided
2 tablespoons chopped shallot
1 small garlic clove, pressed
1/2 cup plus 2 tablespoons olive oil plus additional for brushing
2 large red onions (about l.5 pounds) halved, thinly sliced
1 large red bell pepper
2 large eggplants (2.5 pounds total) cut crosswise into 1/3-inch slices
8 ciabatta rolls, halved horizontally
8 ounces Fontina cheese, sliced
8 large butter lettuce leaves
Whisk 3 tablespoons vinegar, shallot, and garlic in small bowl. Gradually whisk in 1/2 cup oil. Season dressing with salt and pepper. DO AHEAD Dressing can be made 2 days ahead. Cover and chill. Bring to room temperature before using.
Heat 2 tablespoons oil in large skillet over medium-high heat. Add onions; sprinkle with salt. Saute until beginning to brown, about 5 minutes. Reduce heat to medium-low; cook until soft, about 5 minutes. Add 2 tablespoons vinegar and cook until very soft, about 8 minutes longer. Season onion mixture with salt and pepper.
Char bell pepper over gas flame or in broiler. Place in paper bag; seal and let stand 15 minutes. Peel, seed, and cut pepper into VHnch-thick slices. DO AHEAD Onion mixture and roasted pepper can be made 2 days ahead. Cover separately; chill.
Sprinkle eggplant slices lightly with salt. Let stand 30 minutes.
Preheat broiler. Pat eggplant dry. Brush slices with oil and broil until tender, about 3 minutes per side.
Broil rolls, cut side down, until toasted. Turn and place cheese atop bottom half of rolls. Broil until cheese melts, watching carefully to prevent burning. Transfer rolls to work surface. Arrange eggplant atop cheese, then onion mixture and roasted pepper. Drizzle with dressing; top with lettuce leaf and roll top.