Combine first 4 ingredients in a large zip-top plastic bag; seal and shake well to coat. Heat 1 tablespoon oil in a large nonstick skillet over medium-high heat. Add chicken to pan; cook 6 minutes on each side or until done.
Place the remaining 2 teaspoons oil, parsley, and remaining ingredients except bread in a food processor; process 10 seconds or until finely chopped. Tear peasant bread into pieces; add to the processor, and process 4 seconds or until well blended. Thinly slice each chicken breast half, and serve topped with salsa verde.