Between pieces of plastic wrap or waxed paper, place each chicken breast smooth side down; gently pound with flat side of meat mallet or rolling pin until 1/4 inch thick. In shallow dish, mix flour, Parmesan cheese, Italian seasoning and salt. Coat chicken with flour mixture; shake off excess flour.
In 12-inch nonstick skillet, heat oil over medium-high heat. Add chicken; cook about 8 minutes, turning once, until browned on outside and no longer pink in center. Top each chicken breast with 1 slice prosciutto and 1 slice mozzarella cheese. Cover skillet tightly; cook 1 to 2 minutes or until cheese is melted. Sprinkle sage over chicken. Remove chicken from skillet to serving platter; cover loosely with tent of foil, being careful not to let foil touch cheese.
Increase heat to high. Add broth to skillet. Heat to boiling, scraping up any browned bits from bottom of skillet. Boil about 3 minutes or until broth is reduced to about 1/4 cup. Remove from heat; beat in butter. Spoon over chicken.