Thread onion slices onto thin, flat metal skewers (like lollipops). Brush both sides of slices with olive oil.
Grill onion skewers, mushroom cap (gill side down), and the pepper quarters on the rack of an uncovered gas grill or uncovered charcoal grill directly over medium heat for 6 to 10 minutes or just until vegetables are tender, turning once halfway through grilling. Remove from grill and allow to cool.
Meanwhile, in a small bowl, stir together chili powder, salt, garlic powder, paprika, cumin, cinnamon, bittersweet chocolate, allspice, black pepper and cayenne pepper; set aside.
Make a lengthwise cut into the side of each steak, cutting to, but not through the opposite side (it will open like a book). Brush the outsides of the steaks with olive oil; sprinkle the insides and outsides of steaks with the seasoning mixture.
When vegetables are cool enough to handle, remove onion slices from skewers. Cut the grilled onion slices in half. Cut the mushroom and pepper into think strips.
With the first steak "opened", place two slices of cheese on bottom half of steak, staggering the slices so they cover the surface. Layer with half of the vegetables and two more slices of cheese. Close the top half of the steak over cheese and vegetables. Tie together at 2-inch intervals with clean kitchen string. Repeat with the remaining steak, cheese and vegetables.
Place stuffed steaks on the grill. Grill for 14 to 16 minutes or until desired doneness, turning once halfway through grilling. Remove steaks from grill. Cover and let stand for 10 minutes.
Brush the cut sides of the buns with butter. Place buns, cut sides down, on the grill. Grill for 1 to 2 minutes or until lightly toasted.
Remove and discard strings from steaks. Slice the stuffed steaks across the grain into 1/2-inch slices. Divide the stuffed steak slices evenly among toasted buns. Makes 4 sandwiches.