1. Preheat the oven to 450°F. Season the lamb with coarse sea salt (in moderation) and freshly ground pepper. Heat the oil in a large, ovenproof skillet and brown the lamb on all sides.
2. Use tongs to arrange the lamb bone side down. Add the potatoes around the lamb and transfer pan to the oven. Roast lamb until an instant read thermometer inserted in the thickest part of the meat reads 125°F for medium rare, 15 min. Transfer the lamb to a cutting board and allow to rest, loosely covered with foil for 10 min. Place the potatoes in a bowl and loosely cover with foil.
3. While the lamb rests, carefully transfer excess fat from the skillet into a small bowl to be discarded. Place the pan back on the stove over medium heat and add ½ cup wine. Bring to a boil, scraping any bits stuck to the bottom of the pan. Add the rest of the wine, garlic, thyme, and chicken broth. Boil until sauce is reduced to ½ cup, about 8 min.
4. Remove pan from heat, discarding the garlic and thyme. Season with salt (in moderation) and pepper to taste. Strain into a gravy boat and serve with the lamb and potatoes.
Per serving: 679 calories, 52g fat, 21g saturated fat, 104mg cholesterol, 102mg sodium, 17g carbohydrate, 2g fiber, 1g sugar, 23g protein