Place the whole peppers on a sheet pan and place in the oven for 30 to 40 minutes, until the skins are completely wrinkled and the peppers are charred, turning them twice during roasting. Remove the pan from the oven and immediately cover it tightly with aluminum foil. Set aside for 30 minutes, or until the peppers are cool enough to handle.
Meanwhile, combine the olive oil, balsamic vinegar, garlic, salt, and pepper in a small bowl. Set aside.
Remove the stem from each pepper and cut them in quarters. Remove the peels and seeds and place the peppers in a bowl along with any juices that have collected. Discard the stems, peels, and seeds. Pour the oil and vinegar mixture over the peppers. Stir in the capers. Cover with plastic wrap and refrigerate for a few hours to allow the flavors to blend.
To assemble the sandwiches, spread the bottom half of the loaf with the goat cheese. Add a layer of peppers and then a layer of basil leaves. Separate the onions into rings and spread out on top. Sprinkle with salt and pepper. Cover with the top half of the ciabatta and cut into individual servings.