How to Make It
Preheat the oven to 325°. 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 them and braise in the oven until the meat is very tender, about 3 hours.
Transfer the ribs to a platter. Strain the braising liquid, pressing hard on the solids; skim the fat. Season with salt and pepper. Serve half of the ribs with some of the sauce. Reserve the rest in the remaining sauce for sandwiches.