For the short ribs, preheat the oven to 325 degrees F.
Heat 2 tablespoons of the olive oil in a large enameled cast iron casserole. Season the ribs with salt and pepper. Add half of the short ribs to the casserole and cook over moderately high heat until browned, about 6 minutes. Transfer the ribs to a plate. Repeat with the remaining oil and ribs.
Add the celery, carrot and onion to the casserole and cook over moderate heat until softened, about 7 minutes. Add the tomato paste and cook, stirring, until glossy, about 2 minutes. Add the thyme sprigs, anchovies, bay leaf and garlic and cook, stirring, for 2 minutes. Add the stock, wine and vinegar and bring to a boil. Return the short ribs to the casserole, then cover and braise at 325 degrees F for 1 hour. Drop heat to 225 degrees F and cook for 4 more hours or until meat is tender. Remove ribs and strain liquid. Pour liquid back over ribs and let cool overnight in the refrigerator.
For the salad, place all ingredients in nonreactive mixing bowl and toss together.
To serve, skim fat off liquid and reheat ribs in their juice. Remove from pan and reduce liquid by half. Top ribs with liquid and orange salad.