Pulse the cheese, mayonnaise and pepperoncini in a food processor until combined. Season with salt and pepper. Cover and chill at least 3 hours.
Slice the rolls; place a chicken breast on each roll and top with about 2 tablespoons of the cheese mixture. Wrap the sandwiches in foil and keep chilled until ready to use.
Preheat a grill to medium. Place the foil-wrapped sandwiches cheese-side down on the grill and heat through, flipping once, 3 to 5 minutes per side. Serve with your favorite hot sauce.
Photograph by Andrew McCaul
Recipe courtesy Claire Robinson for Food Network Magazine