For the marinade: In a large resealable plastic bag, combine the soy sauce, oil, Worcestershire sauce, lemon juice, garlic, and pepper. Add the flank steak, seal the bag, and refrigerate for at least 8 hours.
Preheat a grill to medium heat.
Drain the steak, discarding the marinade. Place the steak on the grill. Grill 4 to 5 minutes on each side, or until desired temperature. (You may also bake at 425 degrees F until a meat thermometer inserted in thickest portion reads 145 degrees, 40 to 45 minutes.) Let stand for 10 minutes before slicing.
For the bacon horseradish sauce: In a small bowl, combine the green onions, mayonnaise, bacon, horseradish, lemon zest, and lemon juice. Cover and chill.
To assemble: Spread desired amount of Bacon Horseradish Sauce over the bottom of the rolls. Top with desired amount of arugula. Top with sliced flank steak. Cover with roll tops. Serve immediately.
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