In a shallow dish, mix molasses, brown sugar, 1 tablespoon oil and mustard. Add steaks and turn to coat. Cover; refrigerate up to 2 hours.
Drain beef, discarding marinade. Brush mushrooms with remaining oil. Grill steaks, covered, over medium heat 5-7 minutes on each side or until meat reaches desired doneness (for medium-rare, a thermometer should read 135°; medium, 140°; medium-well, 145°). Grill mushrooms, covered, 8-10 minutes or until tender, turning occasionally. Remove steaks and mushrooms from grill; let stand 5 minutes.
Grill rolls, cut side down, for 2-3 minutes or until lightly toasted. Cut mushrooms and steaks into slices. Serve in rolls with cheese.