Put oven rack in middle position and preheat oven to 325°F. Pat ribs dry and sprinkle with kosher salt and pepper. Heat oil in a wide 6- to 8-quart heavy pot over moderately high heat just until smoking. Then brown ribs in batches, without crowding, turning with tongs, about 6 minutes per batch. Transfer to a plate.
Reduce heat to moderate, then cook onion, chopped carrots, and celery in fat remaining in pot, stirring occasionally, until softened and lightly browned on edges, about 7 minutes.
Stir in tomato paste, wine, and vinegar and boil over high heat, uncovered, until liquid is reduced by about half, about 5 minutes. Add stock, water, thyme, and bay leaf and bring to a boil. Add ribs along with any juices accumulated on plate.
Cover pot tightly, then transfer to oven and braise ribs until meat is very tender, 2 1/2 to 3 hours.
Transfer ribs to a platter and discard bones, then let meat stand, loosely covered with a sheet of parchment paper or foil. Pour cooking liquid through a fine-mesh sieve into a bowl (do not press on solids) and discard solids. Let cooking liquid stand, uncovered, until fat rises to surface, about 15 minutes, then skim fat.
While cooking liquid stands, cook lardons in cleaned pot over moderate heat, stirring occasionally, until golden and crisp, about 7 minutes. Then transfer with a slotted spoon to paper towels to drain. Pour off bacon fat from pot, and then add short rib cooking liquid and lardons to pot. Slowly boil, uncovered, stirring occasionally, until sauce is reduced to about 2 cups, about 15 minutes. Season with salt and pepper.
While sauce reduces, boil turnips, baby carrots, and squash separately in a 2- to 3-quart saucepan of boiling salted water , uncovered, until just tender, about 5 minutes for turnips, 6 minutes for carrots, and 6 minutes for squash, transferring each vegetable as cooked with slotted spoon to a bowl of ice and cold water to stop cooking. Drain vegetables and pat dry.
Trim fat and connective tissue from meat, then gently transfer meat (be careful not to break up ribs) and vegetables to sauce and cook over moderate heat, uncovered, until just heated through.
Divide meat and sauce among 8 soup plates, and then top with vegetables.