Cut the chicken breasts in half, as needed, depending on their size. Pound them to about 1/4" thickness and set aside. Mix together the flours, starch, salt and pepper in a large mixing bowl. Set aside. Heat a large skillet over medium-high heat. Add the oil. Once the oil is hot, dredge each breast in the flour mixture and then shake off excess. Saute the chicken breasts in batches, being careful not to crowd the pan too much. Place the cooked chicken pieces on a platter in a single layer and tent with foil to keep warm.
Lower the heat under the pan to medium and add the prosciutto. Saute for a couple minutes, and then add the garlic and shallots. Saute for a few more minutes and then add the mushrooms. Cook until their liquid is evaporated. Season with salt and pepper and then add the wine to the pan. Deglaze (scrape the bottom of the pan clear) and boil for a few seconds. Add the chicken stock to the mixture in the pan and bring to a low simmer. Simmer just a few minutes, to reduce the sauce slightly and then stir in the butter until melted.
Return the chicken breasts to the skillet and simmer for a few minutes, just until the chicken is heated through. Season with salt and pepper. Plate the chicken and top with mushrooms and sauce. Garnish with fresh parsley. Enjoy!