Cut steak lengthwise into 2 pieces. Combine 7 tablespoons olive oil, vinegar, wine, 1/4 teaspoon black pepper, and garlic cloves in a medium bowl, stirring with a whisk. Pour oil mixture into a large zip-top plastic bag. Add steaks to bag; press air out, and tightly seal bag. Turn 3 to 4 times to coat steaks with vinegar mixture, firmly rubbing vinegar mixture into surface of steaks. Refrigerate 4 hours, turning bag 1 to 2 times while marinating.
Heat a large cast-iron skillet over medium-high heat. Coat pan with cooking spray. Remove steaks from bag, and discard marinade. Sprinkle steaks evenly with 1/2 teaspoon salt. Add steaks to pan, and cook 3 1/2 minutes on each side or until desired degree of doneness. Remove from heat. Transfer steaks to a cutting board; let stand for 5 minutes.
While the steaks rest, combine arugula and watercress in a medium bowl. Drizzle with 1 tablespoon olive oil and lemon juice; toss to coat. Divide dressed greens evenly among 4 plates.
Slice steak diagonally across the grain into thin strips; sprinkle evenly with remaining 1 tablespoon oil and remaining 1/4 teaspoon salt. Arrange steak strips evenly over arugula mixture on plates. Sprinkle steak evenly with parsley, chives, and shaved Parmesan. Serve with lemon wedges.