Preheat oven to 425°F. Rub a small roasting pan with oil and place tenderloin in it. Bake tenderloin 20 minutes per pound until the meat reaches an internal temperature of 145°F. Allow tenderloin to rest for 5 minutes prior to slicing.
Slice roll in half and very lightly spread both sides with mayonnaise, if you wish. Top with cheese, pork slices, arugula and fresh pepper.
Close sandwich and grill for about 5 minutes, until cheese is melted and bread is toasted. Remove from grill, cut in half and serve.