Preheat oven to 350 degrees. Dredge ribs in flour, knocking off excess. Heat bacon fat in a 6-quart heavy ovenproof kettle over moderately high heat until hot but not smoking. Brown the short ribs in batches in a single layer without crowding. Transfer short ribs as browned with tongs to a large plate.
Pour off all but about 2 tablespoons bacon fat remaining in kettle and in it cook garlic, onions, carrots, and rosemary with salt and pepper to taste over moderate heat, stirring, until browned lightly. Deglaze the kettle with red wine. Add the beef broth to the vegetable mixture and bring to a boil, stirring. Return ribs to the kettle, squeezing them to fit in a single layer, if possible, and cover kettle with a lid. Braise ribs in oven until tender, about 2 hours.
Transfer ribs with tongs to a platter and keep warm. Pour cooking liquid through a fine sieve set over a saucepan, discarding solids, and skim fat. If necessary, boil liquid to thicken it slightly, and spoon sauce over ribs. Serve with boiled new potatoes.
Recipe courtesy of Gourmet Magazine