1
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Preheat oven to 350°. Season short ribs with salt and pepper. Heat olive oil in a large Dutch oven over medium-high. Brown short ribs on all sides, about 8 minutes per batch. (You will need to brown the ribs in batches.) Transfer short ribs to a plate. Pour off all but 3 Tbsp drippings from pot.
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2
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Add onions, carrots, and celery to pot and cook over medium-high heat, stirring often, until onions are browned, about 5 minutes. Add flour and tomato paste. Cook, stirring constantly, until well combined and deep red, 2-3 minutes. Stir in wine – but taste it first. It is your quality assurance duty as cook, and it is also your reward!
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3
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Add short ribs with any accumulated juices. Bring just under a boil; lower heat to medium and simmer until wine is reduced by half, about 25 minutes. Add all herbs and the garlic to the pot. Stir in stock. Bring back to a simmer, cover, and transfer to oven.
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4
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Cook until short ribs are tender, 2–2½ hours. Transfer short ribs to a platter. Strain sauce from pot into a measuring cup. Spoon fat from surface of sauce and discard. Season sauce to taste with salt and pepper.
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5
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Serve in shallow bowls over mashed potatoes, mashed cauliflower, or polenta. Spoon the sauce liberally over each serving.
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