Lightly pound steak and score on both sides with a knife. Marinate steak in wine and soy sauce for 1 hour.
Remove steak from marinade and pat dry. Discard marinade and lay steak on a flat surface.
Light a grill or start a charcoal fire.
Separate onion slices into rings. Place in a skillet along with vinegar and water. Bring to a rapid boil.
Remove from heat, cover, and let sit for 5 minutes. Drain onion rings.
Place spinach leaves over the flank steak, topping with onion rings.
Roll the steak tightly towards you, tucking meat closely around the vegetables. Tie tightly at 1-inch intervals with kitchen string. Cut the steak crosswise into 5 equal pieces.
Grill 4 to 6 inches from medium-hot coals for 4 to 5 minutes per side, or to desired doneness, turning once. When almost done, sprinkle top of each pinwheel with some of the cheese. Continue to grill for another minute, until cheese melts. Serve immediately.