Prepare a medium hot charcoal fire, preheat a gas grill, or the broiler. Place grill rack or broiler pan 4 inches from heat.
Place cutlets between 2 sheets of plastic wrap and pound to 1/4 inch thickness. (If you don't have a meat pounder or mallet just use an empty wine bottle).
Cut veal into 3 x 2 inch pieces and sprinkle with salt and pepper. Cut mozzarella into 1 x 1/2 inch thick sticks and place a piece of cheese across the center of each cutlet. Sprinkle with parsley and garlic, roll up each piece of veal from one of the short sides.
Skewer rolls onto two metal or bamboo skewers (hold skewers in the same hand, parallel and about an inch apart). Rolls should barely be touching. Skewer all meat in this way.
Brush rolls with olive oil. Sprinkle with bread crumbs, patting them so they stick. Grill/broil skewers, turning once, until meat is browned and the cheese is slightly melted (about 10 minutes).
Slide rolls off skewers and onto a warm serving platter. Serve immediately.