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1
Preheat oven to 325.
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2
Soak the porcini mushrooms in about one cup of boiling water until soft. Lift the softened mushrooms from their soaking liquid and set aside, reserving the mushroom soaking liquid. Roughly chop the mushrooms and set aside.
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3
In a covered braiser or other wide, heavy-bottomed pan with a lid, warm 1 teaspoon of the oil over medium heat until shimmering. Season the oxtails with salt on all sides and add them to the pan in batches, browning them well all over, and adding the remaining oil to the pan as needed. Set the browned oxtails on a plate or platter and set aside.
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4
Add the onion, celery, and carrot to the pan, season with a big pinch of salt, and cook until softened, stirring them to scrape up any browned bits from the bottom of the pan. Clear a spot in the bottom of the pan and add the tomato paste, allowing it to toast for a minute before stirring it through.
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5
Turn off the heat, press down the softened vegetables until they are in a fairly even layer, then add the oxtails back to the pan on top of the vegetables with the cut sides of the bones facing up. Scatter the chopped porcinis and thyme around the pan, and then add the bay leaves, the reserved mushroom soaking liquid (leave any grit behind), 1/4 cup of the port, and the red wine. Cover tightly and place into the oven for 2.5 to 3 hours, until the meat is very tender. Check the oxtails periodically and add a bit of water if the mixture looks dry.
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6
Remove the oxtails and set them aside, covering them with foil to keep them warm. Remove the bay leaves and any thyme stems and discard. Remove the softened vegetables from the pan, pressing them through a fine mesh strainer back into the pan juices. Return the pan to the stovetop and add the remaining 1/4 cup of port, then cook over medium heat for another 10-15 minutes until the sauce is slightly reduced. Add the sherry vinegar and lots of freshly cracked black pepper, stirring through. Return the oxtails to the pan, stirring to coat them in the sauce and re-warm them before serving.
