Season chicken breasts on both sides with salt, pepper and garlic powder. Thinly coat chicken fillets in flour. In a large skillet, heat oil and butter, and cook chicken on medium high heat for about 3 minutes on each side, or until no longer pink in center. Transfer to a plate.
Add chopped onion to the skillet, and cook for a couple of minutes until onion is translucent. Add mushrooms and minced garlic, and cook for about 3-4 minutes until tender and juices have evaporated. Season vegetables with salt and pepper to taste.
Pour Marsala wine, chicken broth and heavy whipping cream to the skillet. Add chopped prosciutto slices. Cook for about 10 minutes, stirring occasionally until sauce has thickened and reduced by half. Season sauce with salt, pepper to taste, if necessary.
Add cooked chicken back to the skillet and warm for a minute. Sprinkle some parsley or fresh thyme and serve warm.