Rinse the turkey pieces and pat dry. Bring 4 quarts of water to a boil in a large pot, along with the onion, carrots, bay leaves, parsley, and salt and pepper. Simmer gently for 20 minutes. Add the turkey pieces and simmer for another 35 to 45 minutes, just until done. Turn off heat, and let turkey cool in the cooking liquid. Discard the skin and bones, shred meat into bite-sized pieces, and reserve. Strain turkey stock and reserve.

Infuse the walnut oil with the paprika by heating the oil in a small saucepan until warm and stirring in the paprika. Leave mixture in a warm area near the stove.

Prepare the walnut sauce: Soak the bread in a little milk until soft, then squeeze it dry and set aside. Grind walnuts in a food processor or blender until fine. Place in a large bowl, and crumble the bread over the walnuts. Add the garlic, onion, paprika, cayenne, salt, and 2 cups of the strained turkey stock. Mix well, and then process in batches in food processor or blender until smooth. Adjust seasonings, adding more stock if necessary to thin sauce.

Mix half of the sauce with the shredded turkey. Arrange the mixture on a serving platter, and pour the remaining sauce over it. Garnish with the walnut halves, and drizzle the walnut-paprika oil over the top. Serve room temperature.