Place the peppers directly on the burner of a gas stove over high heat or on a grill. Just as each section turns puffy and black, turn the pepper with tongs to prevent overcooking. (If you don't have a gas stove, place the peppers on a baking pan, and broil in the oven, turning as each side becomes charred.) Transfer the peppers to a large bowl, and cover immediately with plastic wrap. Let the peppers sweat until they are cool enough to handle, about 15 minutes. Transfer the peppers to a work surface. Peel off the blackened skin, and discard. Cut each pepper in half. Set the four halves aside.
Meanwhile, preheat the oven to 400 degrees. Fold four 18-inch lengths of parchment paper in half, cut into a half-heart shape, and open. Place each chicken breast between two layers of waxed paper, and pound with a meat pounder until 3/8 inch thick. Lay each breast, smooth side down, on a work surface, and season with half the salt and pepper. Divide the prosciutto, and place over each breast. Place a roasted pepper half on top of the prosciutto, and top each with sliced mozzarella. Roll up each breast, and place seam side down, on one half of each parchment heart near the crease. Brush with butter, and season with remaining salt and pepper. Fold the other half of the parchment over the chicken. Make small overlapping folds to seal the edges, starting at the top of the heart. Two inches from the end, twist the parchment twice, gently but firmly, to seal.
Place the packets on a rimmed baking sheet or in a heavy skillet (preferably cast iron), and bake for 30 minutes or until fully puffed. Remove from the oven, and open the packet carefully. Transfer the breasts to a plate, and then spoon the cooking liquid over.
The chicken can be prepared a few hours ahead of time and kept in the refrigerator -- don't place it in parchment until ready to cook, or the paper will get soggy.