

Heat the oil in a large Dutch oven or high-sided skillet over medium-high heat. Season the meat with salt and pepper and then brown it on all sides in batches (so you do not crowd the meat); transfer to a plate. Pour off all but a few tablespoons of fat from the pan.
Reduce the heat to medium and add the carrot, leek, onion and celery to the Dutch oven and cook until the vegetables are tender and just starting to brown, 8 to 10 minutes.
Stir in the garlic, thyme and rosemary sprigs and cook a minute more. Then add the vinegar (watch out, the fumes can be potent) and let it simmer until it reduces by about half.
Heat the oven to 350F. Return the meat to the pot and add enough chicken broth to barely cover. Bring to a gentle simmer on the stovetop, then transfer the pot to the oven.
Braise uncovered in a 350F oven, basting and turning the meat occasionally. Adjust the heat as necessary to maintain a gentle simmer (barely bubbling). The meat is done when it is tender enough to cut with a fork and easily comes away from the bone, about 2.5 hours.
When the ribs are perfectly tender, transfer the meat to a plate, let the liquid cool and spoon off any fat. (For a smooth, refined sauce, strain the liquid). Bring the sauce -strained or not to a simmer and reduce until it thickens enough to coat the back of a spoon. Return the meat to the pot. At this point, the braise can be served right away, refrigerated for up to five days, or frozen for up to three months.
When ready to serve, warm the meat in the sauce, basting frequently and stir in the olives, diced soppressata and chopped rosemary.