Prepare the grill for direct cooking over low heat (250° to 350°F).
Cut the rolls in half lengthwise. Spread an even layer of mustard on the cut side of each roll. Cut the slices of prosciutto into a few pieces and divide them evenly among the bottom halves of the rolls. Cut each slice of provolone in half and arrange those pieces over the prosciutto. Then arrange the peppers and basil leaves on top. Put the top halves of the rolls in place. Press down on each sandwich so it is compacted. Lightly brush each roll on both sides with oil.
Brush the cooking grates clean. Place the sandwiches on the cooking grate over direct low heat. Put a sheet pan on top of the sandwiches and then add two foil-wrapped bricks on the sheet pan. Grill, with the lid open, until the bread is toasted on the bottom, 3 to 4 minutes. Carefully remove the bricks and sheet pan, turn the sandwiches over, replace the pan and bricks, and continue to cook until the bread is toasted on both sides and the cheese has melted, 3 to 4 minutes more.
Transfer the sandwiches to a cutting board and cut them in half, or into smaller pieces if serving as an appetizer. Serve warm.
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