Using the tip of a sharp knife, cut slits 1 inch long and 1/4 inch deep all over the surface of the roast. Insert the garlic slices.
In a shallow baking dish large enough to hold the lamb, whisk together the 3-year aged balsamic vinegar and olive oil. Season to taste with salt and pepper. Add the lamb and turn to coat with the mixture. Marinate 1 hour at room temperature or 2 hours in the refrigerator. Transfer lamb to a work surface and pat dry.
Preheat a convection oven with rotisserie or conventional oven to 375 F. If using a rotisserie, attach lamb to it according to directions, or put lamb in a roasting pan.
Prepare the Potato Tomato Gratin by rubbing the bottom of a medium porcelain gratin dish with the halves of garlic. Arrange the potatoes in a single layer in the dish. Season them with salt, pepper, and sliced garlic. Place the sliced onions in a single layer on top of this. Season as you did the potatoes. Layer tomatoes on top and season the same. Add the white wine and oil.
Place the gratin dish in the oven directly under the lamb, to allow the lamb to turn on the rotisserie and the juices to drip into the gratin.
Cook the roast, basting occasionally with the balsamic vinegar until the meat registers 140 F for medium, about 1 hour. Transfer the lamb to a cutting board and let rest for 10 minutes. Slice thinly and arrange on a warmed platter. Drizzle with aged balsamic vinegar.
Recipe courtesy of La Famiglia Giusti, Modena, Italy.