Heat a grill pan over medium-high heat. Whisk together Worcestershire sauce and oil; brush over steak. Season with salt and a generous grind of pepper. Cook steak, turning once, until medium-rare, 3 to 5 minutes per side, depending on thickness. Transfer to a cutting board; let rest for 5 minutes.
Divide arugula among serving plates. Thinly slice steak across the grain; arrange over arugula. Top with tomatoes and serve.
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