Preheat the oven to 300 degrees. Spray an 8x8 baking dish with cooking spray.
Spray a medium skillet with cooking spray and heat over medium high heat. Season the chicken cutlets with salt and pepper and add to the skillet, cooking 3-4 minutes on each side, until mostly cooked through and golden brown.
4 chicken cutlets, 1 teaspoon salt, 1 teaspoon pepper
Remove the cutlets from the skillet and wrap each with a slice of prosciutto, placing the seam side down into the prepared baking dish. Bake for 15 minutes or until the internal temperature of the chicken is 165 degrees.
4 slices prosciutto
Meanwhile, reduce the heat to medium and add the butter to the skillet. Once melted, add in the shallot and mushrooms. Cook for 5-7 minutes, until the mushrooms are browned. Then add in the garlic and rosemary and cook for 1 minute more.
8 oz mushrooms, 1 shallot, 1 tablespoon garlic, 2 tablespoon unsalted butter, 2 sprigs fresh rosemary
Increase the heat back up to medium high and add in the Marsala wine. Use a wooden spoon to scrape up any browned bits from the pan. Cook for 3-4 minutes or until the wine has mostly cooked off. Then pour in the chicken stock and cook another 3-4 minutes, until all of the liquid has reduced by half.
½ cup Marsala wine, 1 cup chicken stock
Remove the chicken from the oven and nestle back into the pan. Add the thyme and spoon the mushroom sauce over the chicken.
2 sprigs fresh thyme
Place a chicken cutlet on each plate and spoon a generous serving of the mushrooms and sauce over the chicken. Discard the rosemary and thyme.