Combine red peppers, jalapeño, garlic, mayonnaise and vinegar in a food processor and process until smooth. Scrape the mixture into a medium bowl and fold in the olive relish and parsley. Set aside.
Heat the grill to high or the grill pan over high heat. Brush chicken breasts with oil on both sides and sprinkle with salt and pepper, if desired. Grill for 4-5 minutes per side until golden brown and just cooked through.
Remove from the grill, let rest 5 minutes then slice into 1/4-inch slices on the bias.
Spread some of mayonnaise mixture on the bottom half of the bread, add half of the cheese, half of the chicken and repeat with the remaining ingredients (mayonnaise mixture, cheese and chicken in that order).
Spread the cut-side of the top of the loaf with more mayonnaise mixture and place, mayonnaise-side down, on chicken. Wrap tightly in foil, place on baking sheet and place bricks or a heavy cast iron pan on top.
Refrigerate for at least 1 hour (to allow the flavors to meld) or overnight.