Heat the oven to 350°F. In a Dutch oven or high-sided skillet, heat the olive oil over medium or medium high. Season the short ribs with salt and pepper. Working in batches, brown the meat on all sides; transfer to a plate. Pour off all but a few tablespoons of fat from the pan.
Reduce the heat to medium and add the onions, leeks, celery and carrots to the pan. Cook until the vegetables are tender and just starting to brown. Stir in the garlic, thyme and rosemary and cook one minute more. Add the vinegar and simmer until it reduces to 1/2 cup.
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, uncovered, to the oven.
Braise in the oven, basting and turning the meat occasionally for 2-1/2 hours. Adjust the heat as necessary to maintain a gentle simmer (barely bubbling). The short ribs are done when they're tender enough to cut with a fork and and the meat easily comes away from the bone.
Transfer the short ribs to a plate, let the liquid cool, and spoon off any fat. (If you want a smooth, refined sauce, strain the liquid and return to the pot.) Bring the liquid to a simmer and reduce until it thickens enough to coat the back of a spoon. Return the meat to the pot.
When ready to serve, warm the meat in the sauce, basting frequently, and stir in the olives, sopressata, and chopped rosemary.
Make Ahead Tips
The short ribs are even better if made one day ahead. Prepare the braise through the step of reducing the sauce, then return the short ribs to the sauce and refrigerate, tightly covered, for up to five days, or freeze for up to three months. To serve, warm the meat with the sauce and stir in the garnishes.
nutrition information (per serving):
Photo: Scott Phillips