In a heavy-bottomed, 6-quart soup pot, heat the lard and speck until smoking over medium heat.
Add the onions and cook until soft but not brown, about 8 to 10 minutes.
Add the potatoes, 1/2 cup horseradish, chicken stock, cream, and wine and bring to a boil. Boil 15 minutes and lower heat to medium. Cook just below a boil for 1 hour, until the potatoes have fallen apart. Season with salt and pepper and garnish with scallions, remaining fresh horseradish, and poppy seeds.
In a large, heavy-bottomed saucepan, heat the oil over high heat until smoking.
Add all the chicken parts and brown all over, stirring to avoid burning.
Remove the chicken and reserve.
Add the carrots, onions, and celery to the pot and cook until soft and browned. Return the chicken to the pot and add 3 quarts of water, the tomato paste, peppercorns, and parsley. Stir with a wooden spoon to dislodge the browned chicken and vegetables bits from the bottom of the pan. Bring almost to a boil, then reduce heat and cook at a low simmer until reduced by half, about 2 hours, occasionally skimming excess fat.
Remove from heat, strain, and press on the solids with the bottom of a ladle to extract out all liquids. Stir the stock to facilitate cooling and set aside. Refrigerate stock in small containers for up to a week or freeze for up to a month.
