Sprinkle the chicken cutlets evenly with salt and pepper. Top each cutlet with 3 sage leaves and wrap each with 2 strips of prosciutto. Heat the butter and olive oil in a large skillet over medium-high heat. Add the chicken to the skillet and cook for 2 to 3 minutes on each side, or until done.
Meanwhile, combine the chicken broth and cornstarch in a small bowl; set aside. Remove the chicken from the skillet and keep warm.
Add the wine to the skillet and scrape browned bits from the bottom of the pan. Add the chicken broth mixture to the pan, and cook for 2 minutes, or until the sauce thickens.
Spoon the sauce over the chicken and serve.