Slice a pocket horizontally in steak, cutting to within 1/2 inch of but not through opposite side and ends.
Stir together vinaigrette and cumin in a shallow dish or heavy-duty zip-top plastic bag; add steak. Cover or seal, and chill 3 hours, turning occasionally.
Remove steak from marinade, discarding marinade. Place cheese slices in steak pocket. Secure with wooden picks.
Grill steak, covered with grill lid, over medium-high heat (350° to 400°) 7 to 10 minutes on each side or until done. Let stand 5 minutes; remove wooden picks, and cut diagonally into thin slices.
Grill flour tortillas, without grill lid, 1 to 2 minutes on each side or until warm. Serve with steak.
