Microwave bacon on high, 2 to 3 minutes, until done but not crisp; drain on paper towels. Score meat by making shallow diagonal cuts at 1-inch intervals in a diamond pattern. Repeat on other side. Place meat between 2 pieces of plastic wrap. Using flat side of meat mallet, starting at center and working to edges, pound steak into a 12-by-18 inch rectangle. Sprinkle with salt and pepper. Arrange bacon lengthwise on steak. Spread spinach over bacon. Sprinkle with Parmesan cheese. Roll from short side. Secure with wooden toothpicks at 1-inch intervals, starting 1/2-inch from one end. Cut between toothpicks into eight 1-inch-thick slices.
Heat broiler. Place slices, cut sides down, on unheated rack of broiler pan. Broil 3 to 4 inches from heat for 12 to 16 minutes for medium, turning once. Remove toothpicks before serving.