01 - Rub the steak with olive oil, Worcestershire sauce, salt, and pepper in a shallow dish. Let marinate at room temperature for 10 minutes.
02 - Heat a skillet over medium heat. Add butter and sauté the sliced onions and bell peppers until soft and caramelized, approximately 8–10 minutes. Transfer to a plate and set aside.
03 - Increase skillet heat to high. Sear the steak for 2–3 minutes per side for medium-rare, or adjust timing to reach desired doneness. Transfer to a cutting board and rest for 5 minutes before slicing thinly against the grain.
04 - Slice the rolls open and toast lightly until golden.
05 - Mix mayonnaise and Dijon mustard, then spread inside the toasted rolls. Layer arugula, tomato slices, caramelized onions, and bell peppers onto the bottom halves. Top with sliced steak and cheese.
06 - Place sandwiches under a broiler for 1–2 minutes if desired to melt the cheese. Close sandwiches, slice in half, and serve immediately.