In a bowl, add the flour. Set aside.
Lightly season the chicken with salt and pepper. Place 2 sage leaves on one side of each of the chicken breasts. Lay a slice of prosciutto over the sage. Although not required, you may stitch the prosciutto and sage into the chicken with a toothpick.
Holding together the chicken, sage, and prosciutto, dredge the chicken cutlets in the flour, shaking off any excess.
Add the oil and 2 tablespoons of butter to a large skillet set over medium heat. Add the chicken breasts, prosciutto side down, and brown the chicken and prosciutto for about 5 minutes. Flip the chicken and cook an additional 2 minutes. Transfer the chicken to a plate.
Add the remaining butter to the skillet. Add the chicken stock and bring it to a boil. Cook until reduced by half, about 3 minutes.
Return the chicken to the skillet and simmer over medium heat for an additional 2 minutes, spooning some of the sauce on top.
Transfer the chicken to plates, remove the toothpicks, if using, and pour the sauce over top. Serve hot.