In a medium saucepan, mix the sauce ingredients. Bring to a simmer over medium heat and cook for about 1 minute, stirring occasionally.
Lightly coat the steak on both sides with oil. Season evenly, pressing the seasoning into the meat. Allow the steak to stand at room temperature for 20 to 30 minutes before grilling.
Grill the steak over Direct High heat, with the lid closed as much as possible, until cooked to desired doneness, 6 to 8 minutes for medium-rare, turning once. Remove the steak from the grill and let rest for 3 to 5 minutes. Cut the steak in half lengthwise and then crosswise, across the grain, into strips as thin as possible.
Grill the rolls, cut sides down, over Direct High heat until toasted, 10 to 20 seconds. Pile the meat in the rolls. Spoon some sauce on top. Garnish with pickled pepperoncini. Serve right away.