Sprinkle the veal cutlets with salt and pepper on both sides of the meat.
Add the flour to a shallow bowl and dredge the cutlets through the flour, coating both sides of the meat in flour but shaking off the excess.
Add the olive oil to a large skillet and heat over medium heat. Add the floured cutlets to the hot oil and sear for about 2 minutes then flip and cook for another minute to brown the veal. Remove the veal from the pan and set aside.
Add the butter to the skillet and let it melt.
Add the mushrooms to the skillet and toss them in the butter. Cook for about 6 minutes. There should be no water in the pan and the mushrooms should be golden brown and soft.
Add the garlic to the pan and fry for one more minute.
Add the marsala wine to the pan and cook for one minute.
Add the chicken broth to the skillet and stir well, scraping the browned bits off the bottom of the pan. Simmer for about 5 minutes or until the sauce starts to thicken.
Add the veal back to the skillet with the sauce and cook for 2 more minutes.
Serve immediately with a sprinkle of fresh parsley.