Heat a grill pan over medium-high heat. Rub steak evenly with 1 1/2 teaspoons oil; sprinkle with salt and pepper. Add steak to pan; cook 3 minutes on each side or until desired degree of doneness. Remove from pan; let stand 5 minutes. Cut steak across grain into thin slices.
Cut bread in half lengthwise and crosswise. Hollow tops and bottoms of bread, leaving a 1/2-inch-thick shell. Place bread on a baking sheet, cut sides up. Broil 1 1/2 minutes or until toasted.
Place 1 1/2 tablespoons oil, 1/2 cup arugula, parsley, and next 4 ingredients in a food processor. Process until finely chopped. Spread parsley mixture evenly over cut sides of bread. Layer bottom halves of bread with remaining arugula, steak, and tomato; cover with top halves of bread. Cut sandwiches in half.