Combine the red peppers, jalapeno, 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.
1. Heat the grill to high or the grill pan over high heat.
2. Brush the chicken breasts with oil on both sides and season with salt and pepper. Grill for 4 to 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 thick slices on the bias.
3. Spread some of the mayonnaise on the bottom half of the bread, add a few tablespoons of the olive relish, add half of the cheese, half of the chicken and repeat with the remaining ingredients, (mayonnaise, olive relish, cheese, chicken) in that order.
4. Spread the cut-side of the top of the loaf with more of the mayonnaise and place, mayonnaise-side down on the chicken. Wrap tightly in foil, place on a 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.