Place the vinegar, water, sugar, and salt in a medium saucepan over medium-high heat.
Bring to a boil, stirring occasionally to dissolve the sugar.
Place the onion in a heatproof bowl and pour the pickling liquid over it; set aside while you cook the steak.
Arrange a rack about 4 inches from the broiler and heat the broiler to high.
Line a rimmed baking sheet with aluminum foil.
Coat a wire rack with cooking spray and fit over the baking sheet.
Pat the steak dry with a paper towel. Season both sides with the salt and pepper and place on the wire rack.
Broil (the steak should be 1 to 2 inches from the broiler's heating element) for 5 minutes.
Flip the steak and continue broiling until well-browned and charred at the edges, 4 to 5 minutes more for medium-rare, or 6 to 7 minutes more for medium.
Let the steak rest for 10 minutes on the rack.
Whisk the mayonnaise and mustard together in a small bowl.
Drain the onions through a fine-mesh strainer and discard the liquid.
Transfer the steak to a cutting board and thinly slice across the grain.
Spread a thick layer of Dijon mayonnaise on the cut sides of the rolls.
Divide the steak and arugula between the rolls and close them to form sandwiches.