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. Remove ribs from marinade and drain, reserving liquid. Pat ribs dry and sprinkle with kosher salt and remaining 2 teaspoons pepper. Put rack in middle position in oven and preheat to 325°F. 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. Add onions, carrots, celery, and mushrooms to skillet. Over moderately high heat, sauté until onions start to soften, about 15 minutes. 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. 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. Make sauce: