Steps

1. Pat the lamb chops dry. Rub both sides with the cut garlic clove; discard garlic. In a small bowl, stir together 1 tablespoon of the olive oil, all but ¼ teaspoon of the rosemary, and the salt and pepper. Smear the paste over both sides of the lamb. (The chops can be set aside for up to 30 minutes, or refrigerated for several hours.)
2. Heat a heavy skillet over medium-high heat until hot but not smoking. Add the remaining teaspoon of olive oil, and sear the chops 3 to 4 minutes on each side, or until just medium-rare. Transfer the chops to a plate, tent with foil, and let rest while preparing the sauce.
3. Remove the drippings from the skillet. Heat the butter over medium-low heat until the foaming subsides. Add the shallots and remaining ¼ teaspoon rosemary; sauté until the shallots are translucent and just beginning to turn golden, about 2 minutes. Add the port, bring to a boil, and reduce until slightly syrupy, 2 to 3 minutes. Add the stock and vinegar, raise the heat to medium-high, and let reduce by half, 2 to 3 minutes more. Spoon some of the sauce over the chops and serve.