Turn flames on burner to high. Place peppers directly on top of flames and roast, turning often with tongs, until skins are completely black, 5 to 8 minutes. Transfer to bowl and cover tightly with plastic wrap or aluminum foil. Allow to steam for 10 minutes, then peel off and discard skin. Remove stems and seeds and discard.
Cut peppers lengthwise into 1-inch-wide strips and add to bowl. Add balsamic vinegar, capers, garlic, and parsley. Toss gently to combine and season to taste with salt and pepper, adding more vinegar to taste if desired.
Store peppers in the refrigerator in a sealed container for up to three days. Allow to come to room temperature before serving.