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1
One day in advance, trim and season the shortribs: Trim most of the fat from the short ribs, but leave the silverskin and tough sheathing around the bones intact. Salt evenly all over (about 1 scant tablespoon coarse salt per 4 pounds meat). Cover loosely and refrigerate.
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2
Blanch the meat: Pour a few quarts of cold water -- enough to cover the short ribs -- into a deep 6- to 10-quart stockpot. Set over high heat. When the water is warm to the touch, add the short ribs, a teaspoon or so of salt, and bring to a simmer. Simmer for 2 minutes. Drain, rinse the meat in cold water, and wash out the pot.
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3
Assemble and simmer the pot-au-feu: Replace the short ribs in the clean pot and add enough stock so that the meat rises about an inch above the surface. Add cold water to cover by a few inches, bring to a simmer, and skim any last bits of foam that pop up. Taste for seasoning. Add the onions, bay leaves, cloves, peppercorns, star anise, and the thyme, and stir. Cook uncovered at a gentle but very steady simmer, skimming occasionally, for about 1 hour. Skim, then add the carrots, leeks, turnips, and potatoes. Add more stock or water as needed, so everything stays covered. Stir once. Bring to a simmer then taste for seasoning. Simmer until the meat is yielding but not soft, about another hour. The vegetables should be just tender (if they're done before the meat, pull them out so they don't get too waterlogged). Let everything cool in the broth, and refrigerate overnight.
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4
The next day, skim the fat from the top of the broth, then gently reheat the broth with the meat and vegetables. Transfer the meat and vegetables to a shallower pot (with a few ladlefuls of the broth to keep everything moist) and keep warm over gentle heat. Taste the broth and adjust seasoning as needed.
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5
Make the vinaigrette: Chill the tablespoon of broth, then skim any fat. Whisk together the mustard and vinegar in a small bowl, then slowly whisk in the oil. Whisk in a trickle of the cooled pot-au-feu liquid to stabilize this emulsion. Add salt and pepper to taste. Set aside.
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6
To serve: For the first course, ladle the broth into bowls and serve. For the main course, lift the meat from the pot and slide off the bones. Thickly slice across the grain. Arrange on individual deep plates, surrounding with the vegetables, whole, chunked, or wedged. Skim the rich broth and serve a splash of it with each plate. Serve vinaigrette alongside.
