1. Place bread in a food processor; process about 1 minute or to coarse crumbs. Transfer breadcrumbs to a large plate.
2. Place chicken between 2 sheets of plastic wrap; pound to an even thickness. Sprinkle with 1/2 teaspoon salt and 1/4 teaspoon pepper. Brush each chicken breast half evenly with mustard, and roll in breadcrumbs to coat.
3. Heat 1/2 cup oil in a large nonstick skillet over medium heat until hot. Add chicken, and cook 7 minutes on each side or until golden brown and thickest portion registers 165°.
4. Meanwhile, combine lemon juice, parsley, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper in a small bowl. Slowly whisk in remaining 1/4 cup olive oil.
5. Place 1 chicken breast half onto each of 4 plates; top evenly with parsley mixture. Serve immediately with mixed greens.