Spread mayonnaise onto one side of each bread slice. Layer ham, provolone cheese, and roasted red bell pepper onto one slice, then top with the remaining slice, mayonnaise-side down.
Heat a grill pan over medium heat. Place sandwich onto the hot pan. Place another heavy pan onto the sandwich, then add two heavy cans to the top pan. Press down on the cans to compress the sandwich. Reduce the heat to medium and cook for 3 to 4 minutes. Flip the sandwich, replace the pan and cans, and cook until cheese is melted, 3 to 4 more minutes.