Season steak with 1 teaspoon salt and ¼ teaspoon pepper. Heat 1 tablespoon oil in a large skillet over high. Cook steak, turning once, until browned on both sides, 5 minutes per side for medium. Transfer to a cutting board and let rest for 5 minutes before slicing.
Stir together vinegar, mustard, and remaining ¼ cup oil, ½ teaspoon salt, and ¼ teaspoon pepper in a large bowl. Add arugula, pear, and steak and toss to coat. Top with walnuts and blue cheese.