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1
In resealable, 2-gallon plastic bag, place short ribs. Add wine, thyme, parsley, bay leaves, 1 tablespoon pepper, fennel seed, mustard seed, and garlic. Place bag in large bowl and marinate in refrigerate for at least 8 hours and up to 24 hours.
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2
Remove ribs from marinade and drain, reserving liquid. Pat ribs dry and sprinkle with kosher salt and remaining 2 teaspoons pepper.
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3
Put rack in middle position in oven and preheat to 325u00b0F.
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4
In heavy, 12-inch skillet over moderately high heat, heat 1/4 cup oil just until smoking. Working in 3 batches (wipe pan clean and add 1/4 cup oil between batches), sear ribs, turning with tongs, until well-browned on all sides, about 8 minutes total. Transfer ribs, bone side up and in 1 layer, to a 3- to 4-inch deep roasting pan and set aside. Do not clean skillet.
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5
Add onions, carrots, celery, and mushrooms to skillet. Over moderately high heat, saute until onions start to soften, about 15 minutes.
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6
Transfer vegetables to wide, 6-quart sauce pot, making sure to scrape up any brown bits from bottom and sides of skillet. Add reserved marinade and reduce until pan is almost dry, about 1 hour. Add stock and bring to boil. Pour stock mixture over ribs and cover with foil. Transfer to oven and braise until meat is tender and falling off bone, about 2 1/2 hours. Let cool slightly.
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7
When ribs are cool enough to handle, remove any excess fat and discard bones. Transfer beef, reserving liquid, to bowl and cover with foil to keep warm.
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8
Strain cooking liquid through fine-mesh sieve and into medium saucepan, pressing on solids. Discard solids and skim fat. Add carrots and celery and bring to a boil. Continue cooking until reduced to about 2 1/2 cups, about 25 minutes. To serve, spoon braising liquid over sauce, making sure to include carrots and celery, and finish with horseradish.
