Stew chicken gently in covered pot with water, carrot, onion, parsley, salt and pepper for two hours, or until very tender. Skim. You may use the pressure cooker, in which case reduce the water to one quart and shorten the cooking time to 30 minutes under pressure. Let chicken cool in broth. Reserve the stock. Take meat from bones, discarding skin. Dice the meat, or leave it in individual pieces for serving.
Prepare sauce by grinding walnuts twice through the fine blade of the meat grinder. Add paprika to the walnuts and press this in a fine cheesecloth to extract the red oil which will be used later to garnish the dish. Soak bread in chicken stock, squeeze dry and combine with walnuts. Grind three times through the blade of meat grinder, or buzz in the electric blender, slowly adding one cup chicken stock to make a paste. To serve, place the diced or sliced chicken on a serving plattet and spread it with the walnut paste. Sprinkle it with the walnut oil. Some cooks mix the diced chicken with half the walnut paste, reserving the other half to spread on top. Serve this dish cold.