Preheat oven to 350°F. Spray a shallow baking pan with nonstick cooking spray.
Place chicken breast halves between 2 sheets of heavy duty plastic wrap; pound to ¼ inch thickness using a meat mallet or rolling pin. Discard plastic wrap. Top each chicken breast half with 1 slice of prosciutto, 1 slice of cheese, and ¼ cup of arugula (or spinach), leaving a ¼ inch border around the edges. Fold in half, pinching edges together to seal; sprinkle with salt and pepper. (The chicken can be prepared up to a day ahead and refrigerated at this point.)
Dredge chicken in flour, shaking off excess. Heat oil in large nonstick skillet over medium high heat. Add chicken; cook 5 minutes on each side. Place chicken in prepared pan. Bake for 5 minutes or until done.
Notes
You can sub spinach for the arugula, if you wish.
If you are preparing this recipe as GLUTEN FREE just be sure that the brand of prosciutto you are using is designated as GF, and sub GF flour for the all purpose flour.