Start by patting the steaks dry and seasoning them generously with salt and freshly ground black pepper. Heat 2 tablespoons of olive oil in a large sauté pan over medium-high heat. Once the pan begins to smoke lightly, place the steaks in the pan.
Avoid moving them around to get that beautiful brown crust. Sear for about 3-4 minutes on each side until both sides are golden brown. After cooking, transfer the steaks to a plate and set them aside to rest for 10 minutes. Resting ensures the juices redistribute throughout the meat.
While the steaks rest, prepare the salad. Lay the washed and dried arugula across a large serving platter or bowl. Tear the roasted red peppers into large pieces and scatter them over the arugula. This colorful base sets the stage for your delicious dish.
Grab a small bowl and whisk together the remaining olive oil (about 4 tablespoons), balsamic vinegar, and any juices that might have collected on the steak plate. This simple vinaigrette is tangy and ties all the flavors together. Season with a pinch of salt and pepper to taste.
Once the steak has rested, use a sharp knife to slice it into 1 ½-inch thick slices against the grain. Place the slices over the arugula and roasted peppers. Drizzle the balsamic vinaigrette evenly over the salad, making sure every bite is coated with flavor.
Using a vegetable peeler, shave Parmigiano Reggiano directly over the salad. The delicate cheese shavings add richness and balance the tanginess of the vinaigrette. Garnish generously and serve immediately.