Heat a grill pan over medium-high heat. Combine 1 tablespoon vinegar, 1 teaspoon oil, 1/2 teaspoon pepper, and 3/8 teaspoon salt; rub evenly over surface of steak. Coat grill pan with cooking spray. Add steak to pan, and cook for 5 minutes on each side or until desired degree of doneness. Remove steak from pan, and let stand 5 minutes. Cut the steak diagonally across the grain into thin slices.
While steak cooks, combine remaining 2 tablespoons red wine vinegar, remaining 1 teaspoon oil, remaining 1/2 teaspoon pepper, remaining 1/4 teaspoon salt, radishes, and cucumber in a large bowl, and toss well to coat. Add mâche; toss gently to combine. Serve the steak with salad. Sprinkle evenly with cheese.