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.
Recipe courtesy of Paula Deen