Put 1 1/2 quarts of water into a pot with onion, carrots, pepper, salt, bay leaves and parsley. Simmer for 20 minutes. Add chicken and simmer for another 20 minutes. Cool in cooking liquid. Remove chicken from the pot and shred. Strain chicken stock and reserve. Meanwhile infuse walnut oil with paprika by heating oil until warm and stirring in paprika. Leave this mixture on a warm spot on the stove. Soak bread in a little milk until soft. Squeeze dry. Grind walnuts in food processor until fine. Put in large bowl. Crumble in the bread. Stir in garlic, onion, paprika, cayenne, salt and 2 cups of the reserved stock. Mix into a smooth sauce. It should have a thick pouring consistency. If too thick add a little more stock. Mix half the sauce with the chicken. Arragne the mixture on a serving platter and pour remaining sauce over top. Decorate with walnut halves and paprika oil.