How to Make It
In a medium saucepan, heat 1 tablespoon of the oil. Add the garlic and half of the shallots and cook over moderate heat until browned, about 7 minutes. Add the red wine vinegar and boil until almost evaporated, about 2 minutes. Add the wine and boil over high heat until reduced to 1/2 cup, about 10 minutes. Strain into a bowl.
In a small saucepan, heat 1 tablespoon of the oil. Add the chile and the remaining shallots. Cook over moderate heat until softened, about 4 minutes. Add the sugar and 1 tablespoon of water and cook over moderate heat, without stirring, until the water has evaporated and the caramel is richly browned, about 10 minutes. Carefully add the sherry vinegar, stirring, until incorporated. Add the beef stock and boil over high heat until reduced to 3/4 cup, about 8 minutes. Add the red wine reduction and boil over high heat until reduced to 1 cup, about 5 minutes. Season the gastrique with salt and pepper.
Preheat the oven to 450°. In each of 2 large ovenproof skillets, heat 1 tablespoon of the oil. Season the lamb chops with salt and pepper and add them to the skillets, fat side down. Cook over moderately high heat until browned, about 2 minutes. Turn the chops and brown them, about 2 minutes per side. Turn the chops fat side up. Transfer the skillets to the upper and bottom thirds of the oven. Roast the lamb chops for about 7 minutes, or until an instant-read thermometer inserted in the center registers 130° for medium-rare meat.
Let the chops rest for 5 minutes, then transfer to plates. Drizzle with the gastrique and serve with the Moroccan Carrots.