Roast peppers on hot barbecue grill, under oven broiler or even in several toast cycles of a toaster oven. When blackened in spots with loosened skins, cool on a plate. Then peel and seed. Cut into long strips about ½ inch (1 cm) wide.
Discarding ends, slice tomatoes about ¾-inch (2-cm) thick. Lay on a large platter or in large flat container for transporting; 2 platters or containers may be needed. Sprinkle tomatoes with sugar, pinches of coarse salt and grindings of black pepper.
Slice onions into very thin rings. Lay over tomatoes. Top with pepper strips. Whisk oil with vinegar. Pour over tomatoes. Tuck in olives here and there. Sprinkle all with parsley.
Cover and leave to marinate at room temperature for 2 to 3 hours before serving. Do not refrigerate as tomatoes lose flavour and olive oil becomes thick and cloudy. Serve with bread to soak up juices.