Brush peppers with the 3 tablespoons olive oil. For a charcoal grill, place peppers on the grill rack directly over medium coals. Grill uncovered for 25 to 30 minutes or until skins are charred and peppers are tender, turning often to evenly char the skins. (For a gas grill, preheat grill. Reduce heat to medium. Place peppers on grill rack over heat. Cover and grill as above.) Remove the peppers from the grill and wrap in foil. Let stand about 15 minutes or until cool enough to handle.
Carefully squeeze each pepper over a large bowl to collect juices from peppers (do not allow seeds from peppers to fall into the bowl). Using a sharp knife, loosen the edges of the skins from the peppers. Gently and slowly pull off the skins in strips. Halve peppers and remove seeds. Using a knife or your fingers, tear each pepper half into three strips. Place pepper strips in the large bowl with the juices.
In a large skillet, heat the 2 tablespoons olive oil over medium heat. Add garlic; cook about 5 minutes or until garlic is tender. Stir in red pepper strip mixture, vinegar, and brown sugar. Bring to boiling; reduce heat. Cook, uncovered, for 10 to 15 minutes or until most of the liquid is evaporated.
Transfer mixture to a large serving platter; sprinkle with parsley. Serve slightly warm or at room temperature.