Set a large grill pan or cast-iron skillet over high heat. When the pan is very hot, remove the meat from the marinade and season generously with salt and pepper; discard the marinade. Add the beef to the grill pan and cook until nicely browned, 30 seconds per side. Transfer to plates and top with the arugula, mushrooms and Parmesan shavings. Drizzle the dressing over the salads and serve.