In a large saute pan, heat 2 tablespoons olive oil. Season steaks with salt and pepper. When pan starts to smoke, carefully add steaks. Allow the steaks to cook for about 6 minutes on one side, without moving or piercing the meat. This will help create a good, crusty sear. If steak starts to brown too quickly, reduce heat to medium. When steaks are brown, flip and sear the other side for 6 minutes for medium rare. Cook for an additional 3 to 4 minutes per side for medium well. Remove meat to a large plate and allow to rest for 10 minutes.
Decoratively line a large platter with arugula. Tear the roasted peppers into large pieces and scatter over the arugula. In a small bowl, whisk the 1/4 cup extra virgin olive oil, balsamic vinegar and any meat juices that may have collected on the plate from the steaks. Season with salt and pepper.
Slice the steaks across the grain and on a bias into 1 1/2-inch thick pieces. Lay the slices on top of the salad and drizzle with dressing. Using a vegetable peeler, shave about 8 pieces of Parmesan over the dish.