1. Preheat oven to 400°.
2. Combine panko, za'atar, sesame seeds, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a shallow dish. Place eggs and egg white in another shallow dish; lightly beat with a fork. Sprinkle chicken with remaining 1/2 teaspoon salt and remaining 1/4 teaspoon pepper. Dredge 4 breast halves in panko mixture, then egg mixture. Dredge again in panko mixture.
3. Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add 4 coated chicken breast halves to pan. Cook 3 minutes on each side or until lightly browned, turning carefully with a spatula. Place on a baking sheet coated with cooking spray. Repeat procedure with remaining chicken, panko mixture, egg mixture, and oil.
4. Bake at 400° for 10 minutes or until done. Serve with lemon wedges, if desired.