Season the steak generously with salt and pepper and let it sit at room temperature for 20 minutes before cooking.
Heat 1 tbsp olive oil in a heavy skillet over high heat until smoking. Sear the steak for 3-4 minutes per side for medium-rare, or to your desired doneness.
Transfer the steak to a cutting board and let rest for 8-10 minutes, then slice thinly against the grain.
Whisk together the olive oil, balsamic vinegar, honey, Dijon mustard, salt, and pepper in a small bowl until emulsified.
Toss the arugula, cherry tomatoes, and red onion with most of the vinaigrette. Divide among plates.
Top each salad with sliced steak and toasted walnuts, then drizzle with the remaining vinaigrette.
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