Preheat grill for 10 minutes on medium high heat.
Place pork tenderloin on center of grill and close lid. Grill for 10-12 minutes; flip tenderloin and grill 10-12 minutes more or until tenderloin reaches an internal temperature of 145°F or juices run clear. Remove from grill and let rest for 3 minutes before slicing.
Meanwhile, prepare roasted red peppers. If using jarred peppers: drain juices and pat dry with paper towel; slice lengthwise into quarters or thin slices. If using fresh peppers: roast 30-40 minutes in a 450*F oven until slightly blackened/blistered. Cover pan with aluminum foil and let cool for 10 minutes. Once cooled, remove and discard stems, seeds, and skins. Slice roasted peppers lengthwise into quarters or thin slices.
Brush cut sides of Sandwich Potato Rolls with olive oil and grill oiled side-down on preheated grill for 1-2 minutes until lightly toasted with grill marks. Be careful not to burn.
Once tenderloin has rested, cut crosswise into thin slices about ½” thick.
Top grilled Potato Rolls with a handful of arugula, 2-3 slices pork tenderloin, mozzarella cheese, roasted red pepper strips, and basil.