1. Combine tomatoes, onion and 1/4 teaspoon salt in a large bowl.
2. Whisk egg and egg white in a shallow dish. Combine breadcrumbs, grated cheese and parsley (if using) in another shallow dish. Season steak with the remaining 1/4 teaspoon salt and 1/4 teaspoon pepper. Dip each piece into the egg, allowing excess to drip off into the dish, then dip in the breadcrumb mixture and turn to coat.
3. Heat 2 teaspoons oil in a large nonstick skillet over medium heat. Add the steaks and cook until golden brown on the first side, about 3 minutes. Turn the steaks over, add 1 teaspoon oil and cook until the steaks are cooked through, 3 to 4 minutes more. Transfer to a plate; tent with foil to keep warm.
4. Add 1/4 cup shaved cheese to the tomato mixture. Add the remaining 1/4 teaspoon pepper, the remaining 3 teaspoons oil, arugula, basil and lemon juice; toss to combine. Serve the steaks on beds of the arugula-tomato salad. Garnish with lemon wedges.