Preheat the oven to 400˚F

Set a 12-inch sauté pan over medium-high heat.  Season the lamb with 1 tablespoon of salt and 1½ teaspoons of the black pepper.  Add 1½ teaspoons of the oil to the sauté pan and place the lamb, fat side down, in the pan.  Sear the lamb until the fat has rendered and the skin is golden brown, about 3 minutes.  Continue to cook the lamb, turning to cook evenly on each side, about 2 minutes each side. Transfer the pan to the oven and cook until the lamb is rare, about 5 minutes. 

Make the sauce while the lamb is cooking: Set a 1-quart sauce pan over medium heat and add the remaining 1½ teaspoons of olive oil.  Once the oil is hot, add the shallots to the pan and sweat until translucent, about 1 minute.  Add the garlic to the pan and sweat for 30 seconds.  Pour the balsamic vinegar into the pan and bring to a boil.  Allow the balsamic to gently boil and reduce until only about ¼ cup of balsamic remains, about 10 minutes.  Add the veal reduction to the pan, as well as the rosemary and the remaining teaspoon of salt, and ½ teaspoon of black pepper.  Bring the sauce to a boil and cook for 3 to 4 minutes.  Remove from the heat and swirl the butter into the pan.  Remove the rosemary from the sauce before serving.

When the lamb is rare, remove from the oven and let rest for 5 minutes before serving. To serve, slice each double chop in half, and drizzle with the balsamic reduction.