Bring the beef steak to room temperature and season with salt and pepper. Heat half a tablespoon of olive oil in a hot pan and sear the beef steak briefly, about two minutes per side for rare. Let the meat rest.
Arrange the arugula on a plate. Roughly chop the walnuts and scatter them over.
Slice the rested beef steak into thin strips and place these on the salad.
Make a dressing from the remaining olive oil, a splash of balsamic vinegar, salt and pepper. Drizzle the salad and shave parmesan over it. Serve immediately.