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Preheat the oven to 300°F.
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Heat the oil in a heavy large pot over medium high heat.
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Season the beef on all sides with salt and pepper.
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Add the beef to the pot and cook until golden brown on all sides, about 12 minutes. Transfer the beef to a plate.
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Reduce the heat to medium and add the shallots to the pot.
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Sauté until the shallots are golden, about 2 minutes.
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Add the carrots, celery, and garlic and sauté for 3 minutes.
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Add the wine, vinegar and simmer until the liquids are reduced by half, stirring to scrape up any browned bits on the bottom of the pot, about 5 minutes.
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Stir in the beef stock, thyme, rosemary, and bay leaves. Return the beef to the pot.
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Bring to a simmer, then cover the pot and transfer it to the oven.
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Braise until the beef falls apart with a fork, about 2 ½ - 3 hours.