Bring the chicken stock to a simmer and add the chicken breasts. Add some water if there is not enough liquid to cover the meat. Simmer gently for 10 minutes, then turn off the heat.
Meanwhile, heat the olive or walnut oil in a small pot over low heat and add the paprika. Stir well to combine. Heat until you can smell the aroma of the paprika, then turn off the heat.
Tear the bread into chunks and put into a bowl. Ladle out about a cup or two of the chicken broth and pour it over the bread.
Set aside ½ cup of walnuts and put in a bowl with the green onions and 1 tablespoon of the parsley.
Put the rest of the walnuts into a food processor with the garlic, the cayenne, about a teaspoon of salt, the rest of the parsley and the soaked bread. Buzz to make a thick, relatively chunky paste. If it needs a bit more chicken broth to loosen up, add some a tablespoon at a time.
Stir the paprika-oil, then pour it into the food processor and buzz to combine. Taste the mixture to see if it needs salt.
Pull the skin off the chicken breasts and tear the meat into shreds. Put it in the bowl with the unchopped walnuts, green onions and such.
Add the walnut-paprika paste from the food processor to the bowl and stir gently to combine everything thoroughly. Add black pepper and lemon juice to taste and stir one more time to combine.