Cover chicken bones with cold water and over medium heat, bring to a simmer. Strain through a colander, discarding liquid. Rinse the bones with cold water and place back in pot. Add 6 quarts water and place over medium heat. Slowly bring to a boil, skimming any fat or impurities that rise to the surface. Reduce heat and simmer for 1 1/2 hours, adding more water if needed to keep bones covered. Add the vegetables and herbs and let simmer for 1 hour more, skimming frequently. Put the stock through a fine strainer and chill.
Place raw veal bones in a large pot. Cover with cold water and slowly bring to a boil over medium heat, skimming fat and impurities that rise to the surface. When the water reaches a boil, immediately drain through a colander; discard the liquid. Rinse the veal bones under cold water and return to the clean pot. Cover with 10 quarts water.
Chef's note: Keep the pot offset on the burner to cause the fat and impurities to gather on one side, making it easier to skim.
Return to medium heat, skimming frequently and bring to a bare simmer for 2 hours. Place the tomato paste in a mixing bowl and whisk hot broth into the paste until thinned to a pourable consistency. Add the paste mixture back to the stock and simmer 3 hours more, continuing to skim. Add more water if needed to keep the bones covered. Add the vegetables and herbs and simmer 1 hour more. Strain the liquid into another pot. Reserve the bones for a second veal stock. Return the pot of strained stock to a low simmer and slowly reduce by one-fourth.
Preheat oven to 225 F. Thoroughly season short ribs on all sides with salt and pepper; refrigerate and allow to sit 6 hours or overnight. Heat the oil in a heavy skillet over high heat and brown the ribs on all sides, about 2 minutes on each side. Brown ribs in several batches, if needed, to avoid overcrowding the pan. Transfer ribs to a roasting pan. In the same skillet, brown the onion, carrot and celery, about 5 minutes; add to the roasting pan with the ribs. Place red wine and Madeira wine in a separate pot and bring to a boil for 5 minutes to remove the raw alcohol flavor. Pour wine, chicken stock and veal stock over the ribs. The liquid should come about three-fourths of the way up the sides of the ribs. Add the thyme and cover roasting pan with aluminum foil. Braise in oven for 6 hours on the middle rack. When done, meat will practically fall off the bone; let cool to room temperature. Strain off most of the braising liquid with a chinois into a 4-quart nonreactive pot, leaving enough liquid to keep ribs moist. Bring strained liquid to a simmer, skimming frequently until reduced by half, about 1 hour.
Pick the leaves from the Italian parsley, wash and dry. Add lemon peel and horseradish to the parsley and chop together.
Chef's note: Prepared horseradish can be used, but reduce amount to 1 teaspoon.