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.