Place chicken between two sheets of wax paper; using a rolling pin, pound chicken to 1/4-inch thickness. (To watch a video of this technique, click here.)
Rub chicken with 1/4 teaspoon each pepper and salt. Evenly divide prosciutto and cheese over chicken; fold chicken in half to cover prosciutto and cheese and press down to hold shape.
In a shallow bowl, combine bread crumbs, parsley and remaining 1/4 teaspoon pepper. Place flour on a plate. In another shallow bowl, whip egg whites until soft peaks form.
To coat chicken, dredge each piece of chicken in flour; turn to coat. Then dip each chicken breast in egg whites; turn to coat. Next, dredge chicken in bread crumb-mixture and press down to make sure all sides are covered. Repeat until all four chicken breasts are coated.
Coat a large skillet with cooking spray and set over medium-high heat; add butter and oil. When they begin to shimmer (about 1 or 2 minutes), place chicken in a single layer in skillet; cook, flipping once, until nicely browned and chicken is completely cooked through, about 6 to 8 minutes. Serve immediately. Yields 1 chicken breast per serving.