Heat a cast-iron skillet on medium-high to high and add olive oil. When oil begins to simmer, place steak in skillet and do not move for 5 minutes. Turn it once, and cook for another 3 minutes to medium-rare (or more or less depending on preference).
On a grill:
Prepare a grill for direct-heat cooking over hot charcoal or high heat for gas. Oil grill rack, then grill steak, covered only if using a gas grill, turning once, 4 to 6 minutes total for medium-rare.
Transfer steak to a cutting board and let rest, loosely covered with foil, for five minutes. Arrange arugula on a platter. Thinly slice steak on the diagonal, across the grain. Arrange over arugula, then toss remaining ingredients on top. Drizzle dressing on top and serve.