Place steak in a shallow dish or heavy-duty zip-top plastic bag; pour 1/2 cup Apple Barbecue Sauce over steak. Cover or seal, and chill 8 hours.
Remove steak from marinade, discarding marinade.
Grill steak, covered with grill lid, over medium-high heat (350° to 400°) 7 minutes on each side or to desired degree of doneness.
Cut steak diagonally across the grain into thin strips. Serve on rolls with tomato, lettuce, and, if desired, onion. Drizzle with remaining sauce; sprinkle with pepper.
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