Place chicken, onion, bay leaf, salt and water in a saucepan. Simmer gently for 25 to 35 minutes, until the chicken is fully cooked.
Remove the chicken and strain the broth. Reserve the broth for the sauce.
Shred the chicken finely with two forks or your fingers.
Moisten stale bread with warm chicken broth and let it soften.
Blend walnuts, softened bread, garlic, olive oil, salt, pepper and 1 cup of broth until creamy.
Add more broth gradually if the sauce is too thick.
Mix the shredded chicken with the walnut sauce until evenly coated.
Transfer to a serving plate, smooth the top and chill for at least 1 hour.
Warm oil in a small pan and briefly stir in red pepper flakes or paprika.
Drizzle the pepper oil over the chilled chicken and garnish with walnuts and parsley.