Step 1In a pot of boiling salted water, cook the green beans until crisp-tender, about 4 minutes. Drain. Transfer the beans to a bowl of ice water and cool. Drain.
Step 2Prepare a grill (to medium-high heat). Combine the green beans, arugula, tomatoes and olives in a large bowl. Whisk olive oil and vinegar in a small bowl to blend. Season the dressing to taste with salt and pepper.
Step 3Brush the steaks with the remaining 1 tablespoon olive oil; sprinkle them with salt and pepper. Grill the steaks to desired doneness, about 1 1/2 minutes on the first side and 1 minute for the second side for medium rare. Transfer the steaks to a work surface; let stand 5 minutes. Cut the steaks crosswise into thin strips.
Step 4Toss the salad with enough dressing to coat. Divide the salad among six plates. Top with steak strips. Sprinkle cheese over.