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1
Place the mushrooms in a small bowl. Bring 1 cup of the water to a boil. Pour over the mushrooms. Let stand for 30 minutes to soften.
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2
Remove the mushrooms from the soaking liquid, squeezing as much liquid as possible back into the bowl. Coarsely chop the mushrooms.
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3
Strain the soaking liquid through a coffee filter or 2 layers of cheesecloth. Set aside.
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4
Preheat the oven to 400 degrees.
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5
Heat 2 tablespoons of the oil in a heavy large Dutch oven over medium heat. Add the onions and saute for about 10 minutes, until translucent.
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6
Reduce heat to low. Cook for about 15 minutes, until the onions begin to brown, stirring from time to time.
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7
Add the vinegar and cook, stirring, for about 10 minutes, until the onions turn a deep golden brown.
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8
Add the wine and bring to a boil, scraping up any browned bits in the pot. Transfer the mixture to a bowl.
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9
Heat the remaining 2 tablespoons oil in the same Dutch oven over high heat. Season the brisket with salt and pepper. Brown well on all sides. Transfer the meat to a platter.
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10
Add the mushroom-soaking liquid to the Dutch oven and bring to a boil, scraping up any browned bits.
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11
Return the brisket to the pot, along with the onion-wine mixture, the remaining 3 cups water, the mushrooms, garlic, thyme and bay leaves. Bring to a boil.
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12
Tightly cover the pan. Place in the oven and cook for about 3 hours, until the brisket is very tender.
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13
Transfer the meat to a platter and tent with foil.
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14
Remove the bay leaves from the cooking liquid. Working in batches, puree the cooking liquid in a processor until smooth. Transfer to a large saucepan. Adjust seasoning and rewarm, if necessary.
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15
Cut the brisket across the grain into thin slices. Arrange on a platter. Spoon the sauce over the meat.