Rub 2 tablespoons of extra-virgin olive oil over the rib-eye steaks.

Sprinkle the steaks with 1 teaspoon each of kosher salt and freshly ground black pepper.

Heat 1 tablespoon of extra-virgin olive oil in a large saute pan over medium-high heat.

Add the steaks to the hot pan and sear for about 5 minutes per side for medium-rare, ensuring a good crust by not moving or piercing the meat.

Transfer the seared steaks to a large plate and let them rest for 10 minutes.

Line a large platter with fresh arugula.

Tear the roasted red bell peppers into large pieces and scatter them over the arugula.

In a small bowl, whisk together the remaining 4 tablespoons of extra-virgin olive oil, balsamic vinegar, 1/2 teaspoon each of salt and pepper, and any accumulated steak juices.

Season the dressing with more salt and pepper to taste.

Cut the rested steaks across the grain and diagonally into 1 1/2-inch-thick slices.

Lay the steak slices atop the arugula and peppers.

Drizzle the salad with the prepared balsamic vinaigrette dressing.

Using a vegetable peeler, shave Parmesan cheese over the salad.

Serve immediately.