Season meat with salt and pepper. Top each slice of meat with a slice of prosciutto. In a medium bowl, moisten bread crumbs with milk. Add grated cheese, onion, parsley, arugula, salt and pepper to the crumbs and combine well. Spread a thin layer of stuffing down the center of each beef slice and roll tightly. Fasten rolled meat with plain toothpicks.
Heat a large nonstick skillet over medium high heat. Add oil to a hot pan along with garlic. Set meat into pan and brown on all sides, 6 minutes. Remove the meat from the pan. Add butter to the pan. Add mushrooms to the melted butter. Saute mushrooms 5 minutes. Add flour to the pan and cook 2 minutes. Whisk wine into the flour and mushrooms and scrape up pan drippings. Reduce wine 1 minute, then whisk in beef broth and tomato paste. Set meat back into sauce and reduce heat to medium low. Partially cover pan with a cover left ajar an inch. Simmer meat in sauce 10 to 15 minutes. Transfer beef rolls to a platter, removing toothpicks. Pour pan gravy down over the beef rolls and serve.