Preheat the oven to 325 degrees F.
Season the ribs with salt and pepper. Dust with the flour. Heat the oil in a large braising pan or ovenproof casserole over medium-high heat. Add the bacon and cook until most of the fat is rendered, then remove and set aside.
Add as many ribs as can fit in a single layer to the pan. You will need to cook them in batches. Sear the ribs on both sides until well browned, then remove from the pan and set aside. Repeat with the remaining ribs. Discard all but 2 tablespoons of the fat from the pan.
Lower the heat to medium, add the carrots and onions, season with salt and pepper, and saute until the vegetables begin to brown, about 10 minutes. Add the garlic and tomato and paste and cook for 4 more minutes, scraping the browned bits off of the bottom of the pan with a wooden spoon. Add the red wine and brandy and reduce by 1/2, about 6 minutes.
Return the ribs and bacon to the pot. Add the remaining ingredients except the apricots and parsley and bring to a boil. The liquid should come 1/3 of the way up the ribs, if it does not, add some water. As soon as the liquid comes to a boil, turn off the heat an cover the ribs tightly with foil, pressing the foil down into the pan, then place a lid on the pan.
Braise the ribs in the oven for 2 hours, turning them every 30 minutes so they cook evenly. Add water as necessary to keep the braising juice 1/3 of the way up the ribs.
After 2 hours, add the apricots and cook for an additional 30 minutes. The meat should be almost falling off the bones (if it is not, keep cooking until it does). Transfer the short ribs to a large platter. Spoon the vegetables, olives, and apricots over them. Keep warm.
Strain the braising juices into a clear glass container and siphon or skim off the fat. The braising juices may already be the consistency of a sauce. If not, return them to the pan and boil for a few minutes to thicken. If you prefer an absolutely smooth sauce, strain out any remaining pieces of vegetable. Taste, season with salt and pepper, and add the parsley. Pour the sauce over the ribs and serve immediately.
Recipe courtesy of Jody Adams