Place chicken breasts on a large enough piece of plastic wrap to pull up and cover the top of the chicken. Pound each breast between the plastic wrap with a meat mallet until about 1 ½ inches thick.
Place prosciutto over the top of each breast to cover. Top with plastic wrap again and pound with meat mallet to incorporate the prosciutto into the breast.
Heat 1 Tbsp EVO over medium heat in a skillet large enough to contain both breasts. When the oil is heated add the chicken, prosciutto side down to the pan. Cook about 3-4 minutes per side, or until golden brown. Remove to platter and keep warm.
In the same skillet add the last tablespoon of EVO and the butter. When the butter has melted add shallots and mushrooms. Stir occasionally and cook about 3-4 minutes until the shallots and mushrooms are soft and fragrant.
Add sage and rosemary to the skillet and season with a little salt and pepper. Stir for about 30 seconds and pour in Marsala and broth. Cook until reduced by half, about 7-10 minutes.
In a small cup or bowl, mix about 1 ½ Tablespoons of the flour with some of the liquid from the skillet to make a roux. Mix this back into the skillet to thicken the sauce. Stir to combine.
Plate the chicken and ladle sauce over the top. Enjoy!