Let the beef sirloin rest at room temperature for at least 30 minutes to ensure even cooking.
Heat a skillet over high heat and lightly coat with olive oil. Season the steak generously with salt and pepper on both sides.
Sear the steak in the hot skillet for 2-3 minutes per side for a medium-rare finish. Cook for an additional 1-2 minutes per side if you prefer it more well-done.
Remove the steak from the skillet and let it rest for 5 minutes to allow the juices to redistribute throughout the meat.
Meanwhile, prepare the arugula: wash and thoroughly dry it. In a bowl, whisk together the olive oil, balsamic vinegar, and lemon juice. Drizzle the dressing over the arugula.
Slice the rested steak thinly against the grain and arrange it over the bed of arugula. Sprinkle with parmesan shavings and a pinch of freshly ground black pepper to taste.
Serve immediately, garnished with fresh lemon wedges.
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