Gently pound the chicken breasts, one at a time, between sheets of waxed paper or parchment paper with a rubber or wood mallet or the side of an empty wine bottle until they are very thin -- 1/4-inch thick and about 5 inches wide and inches long. Season the top of each piece of chicken with salt and pepper. Lay a slice of ham and a slice of cheese horizontally along the bottom half of each breast, fold a 1/2-inch strip of each side inward and then fold the top over to enclose the filling completely.

Mix the parsley, rosemary and sage together in a wide shallow bowl or pie plate. One at a time, put a filled chicken breast in the herb mixture, press to adhere as many herbs as you can, then turn and coat the other side with herbs. Coat all the breasts with herbs and set them on a plate until ready to cook. At this point they can be covered with plastic wrap and stored in the refrigerator for up to 24 hours.

Heat the oil in a large skillet or saute pan over medium-high heat. Season the herbed, stuffed breasts with salt and pepper. When the oil is hot, carefully lower the chicken into the pan, reduce the heat to medium, and cook, uncovered, until the underside is a deep brown color, about 5-6 minutes. Turn the chicken over and cook on the other side until well browned and the chicken is cooked through, another 5-6 minutes. Transfer the chicken to a warm platter and serve hot.