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Heat a large Dutch oven over medium high heat for several minutes, add butter and olive oil and let foam up.
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Grab one piece of ox shank dredge one side in flour, shake off excess, repeat with other side, then carefully transfer to Dutch oven to brown. Repeat with remaining shank(s), making sure not to crowd the pot. Go one at a time if you must.
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Brown shanks for a couple of minutes on each side, until golden brown and delicious.
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Once browned on both sides, remove ox shanks from Dutch oven and set aside while you sautée the vegetables.
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Add carrots to Dutch oven and leave relatively undisturbed to caramelize, about 2-3 minutes.
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Add onions to the pot and leave once again relatively undisturbed to brown and caramelize, about 2-3 minutes.
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Add celery and brown for another minute or so.
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Add tomato paste and fry for about a minute.
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Add red wine and stir to deglaze the bottom of the Dutch oven.
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Nestle the shanks back into the pot, add thyme, bay leaves, garlic, whole pepper corns and the whole, canned tomatoes.
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Cover with a lid and place in oven to cook low and slow for four hours.
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When ready to serve, return to cook top and adjust seasoning with salt and pepper as needed, add a generous glug of sherry vinegar to cut the richness and sweetness of the dish.
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Lastly, carefully fish out the bay leaves. They’re not good eats!