Heat oil in a large nonstick skillet over medium-high heat. Sprinkle chicken with Italian seasoning, salt, and black pepper. Add chicken to pan, and cook 3 minutes on each side.
While chicken cooks, place broth, vinegar, and bell peppers in a food processor; process until smooth. Add bell pepper mixture to pan; bring to a boil. Cover, reduce heat, and simmer 3 minutes. Uncover and simmer 3 minutes or until chicken is done. Sprinkle servings evenly with cheese. Garnish with parsley, if desired.