For the Beef: Combine the balsamic vinegar, rosemary and garlic in the bowl of a food processor, and pulse until the rosemary is finely chopped. Add the olive oil and pulse until all the ingredients are combined. Season marinade with salt and pepper.
Place the steaks in a large bowl or nonreactive baking dish. Pour the marinade over and turn to coat them on all sides. Cover tightly with plastic wrap and refrigerate for at least 1 hour and up to overnight. Remove the steaks from the refrigerator and bring to room temperature before grilling.
Preheat grill pan or heavy-bottomed skillet over high heat.
Remove the steaks from the marinade, discard the marinade, and generously season the steaks with salt and pepper on both sides, using about one teaspoon of salt per pound of meat.
Put the steaks on the grill pan and cook until the meat is seared and deep brown on all sides, 5 to 6 minutes per side for medium rare. Remove the steaks to a platter or cutting board and let them rest for about 5 minutes before slicing. Use a sharp knife to carve the steaks diagonally against the grain into 1/2-inch thick slice.
While the steaks are resting, use a large knife or mandoline to cut the wedge of Parmiagiano-Reggiano into very thin slices. Put the arugula in a large, wide bowl, sprinkle with salt and toss gently to distribute evenly. Drizzle the vinaigrette and toss gently to coat the leave. Taste for seasoning and add more salt or vinaigrette, if desired.
To serve plate steak with dressed arugula on the side. Drizzle with the balsamico condimento and olive oil.
Shave porcini mushrooms and Parmiagiano-Reggiano onto the dish.
For the Lemon Vinaigrette: Combine the shallots, lemon juice and zest, vinegar, and salt in a small bowl. Set the bowl aside for 5 to 10 minutes to marinate the shallots. Add the olive oil in a slow, steady, stream, whisking constantly to combine. Stir in the pepper. Taste for seasoning and add more salt or pepper, if desired.