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1
Put oven rack in middle position and heat oven to 300 degrees.
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2
Pat brisket dry, prick all over fatty side with fork, and cut into 2 roasts (important for liquid reabsorption later). Season with salt and pepper.
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3
Use 2 skillets to brown both roasts at once. Heat oil in 12-inch skillets over medium-high heat until just smoking. Brown roasts on both sides (10-14 minutes). Transfer fat side up to a single 13 by 9-inch baking dish.
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4
Meanwhile, microwave 3/4 cup water and porcini in covered bowl until steaming (1 minute). Let sit until softened (5 minutes). Drain porcini through strainer lined with coffee filter, reserve liquid, and mince and reserve porcini.
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5
Scrape browned bits from roasts into single skillet, and pour off all but 1 tablespoon fat. Add mushrooms and 1/4 teaspoon salt and cook medium-high until liquid evaporates and mushrooms are golden brown (8 minutes).
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6
Add onions and sugar, and cook until browned (8-10 minutes).
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7
Add flour, garlic, and thyme, and cook until golden and fragrant (1 to 2 minutes).
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8
Slowly whisk in broth, wine, 1/2 cup reserved porcini liquid, reserved porcini, and bay leaves, scraping up any browned bits, and bring to boil. Reduce heat to medium and simmer until thickened, about 8 minutes.
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9
Pour sauce over roasts and cover dish tightly with aluminum foil. Bake until tender and fork inserted into meat meets no resistance, 41/2 to 5 hours.
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10
Let brisket cool in dish at room temperature, uncovered, for 1 hour, flipping halfway through cooling. Discard bay leaves. (Cooled brisket can be refrigerated in sauce for 2 days; reheat gently, covered, in 300-degree oven for 1 hour before proceeding with next step.).
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11
Transfer roasts to carving board. Strain sauce through fine-mesh strainer into fat separator; reserve mushrooms. Let liquid settle, then pour into bowl. Stir vinegar into sauce and microwave until warm, 30 to 60 seconds.
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12
Slice roasts against grain into 1/4-inch slices and return to dish with mushrooms. Pour 11/2 cups sauce over meat. Serve with remaining sauce.
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13
(Refrigerate sliced brisket in sauce for up to 3 days; reheat meat in sauce.).
