Place peppercorns, thyme, parsley and bay leaf in a small square of double-ply cheesecloth. Bundle at top and tie with kitchen string; set aside.
Stir together paprika, thyme, salt, pepper and cayenne pepper in large shallow bowl. One at a time, coat each piece of short rib in spice mixture.
Preheat oven to 350°F.
Add onions, carrots, celery and garlic along with 2 tablespoons cold water to the roasting pan. Cook over stovetop, stirring to scrape up any browned bits from bottom of pan, for about 4 minutes or until vegetables have softened. Stir in wine and tomato paste. Bring to a boil. Boil for about 15 minutes or until wine is reduced to about 1/3 cup, barely covering the vegetables. Pour in the stock and bring to a boil.
Pour stock vegetable mixture over ribs. Cover pan tightly with aluminum foil. Bake in center of preheated oven for two and a half hours or until meat is fall-off-the-bone tender. If serving right away, skim off as much excess fat as possible. (Meat can be slightly cooled and refrigerated overnight. Skim off any solidified fat. Rewarm in a 325°F oven for one hour).
In large heavy saucepan or skillet, heat oil over medium-high heat. Add ribs, about three at a time, and brown well on each side, about 12 minutes total. Remove ribs to roasting pan large enough to hold them in a single layer.
Whip oil based non-dairy whip topping to soft peaks.
Drain horseradish; fold cream into horseradish.
Serve with meat.