Put the Chukar breasts side by side on a cutting board and lay a piece of plastic wrap over them; carefully pound with a flat mallet, until they are about 1/4-inch thick. Chukar is very delicate so be careful not to break them apart. Put some flour in a shallow platter and season with salt and pepper; mix with a fork to distribute evenly. Heat the olive oil over medium-high flame in a large skillet. When the oil is nice and hot, dredge both sides of the Chukar cutlets in the seasoned flour, shaking off the excess. Place the cutlets into the pan and fry for 3-4 minutes on each side or until golden, turning once. Do this in batches so that the breast fit comfortably in the pan without touching. Remove the Chukar to a large platter in a single layer to keep warm.

Lower the heat to medium and add the prosciutto to the drippings in the pan and saute for 1 minute to render out some of the fat. Now, add the mushrooms and saute until they are nicely browned and their moisture has evaporated, about 5 minutes; season with salt and pepper. Pour the Marsala in the pan and boil down for a few seconds to cook out the alcohol. Add the chicken stock and simmer for a minute to reduce the sauce slightly. Stir in the butter and return the chicken to the pan; simmer gently for 1 minute to heat the chicken through. Season with salt and pepper and garnish with chopped parsley before serving. This dish can be served with Orzo Pasta or Risotto.