Start by preparing your ingredients. Place the diced red onion in a small bowl and cover with cold water. Let it soak for 20 minutes (or longer) to make it less pungent and then drain the water away.

Toast the walnuts by tossing them in a dry skillet over medium heat for 5 to 10 minutes or on a sheet pan in the oven at 350ºF for 10 minutes. Set the toasted walnuts aside.

Poach the chicken breasts by bringing a large pot of water to a boil. Season the water with salt and add the chicken breasts. Let the water return to a boil and then simmer for 2 minutes. Turn the heat off, cover the pot with a lid and let the chicken sit for 20 minutes. Transfer the chicken to a cutting board. Let it cool for 10 minutes, then cut the chicken into bite-sized pieces or shred the chicken with two forks. Place the chicken in a large bowl.

Drain the red onion and pat it dry with a clean paper towel. Add the onion to the bowl with the chicken, along with the toasted walnuts, celery, apples, dried cranberries and parsley.

Combine the mayonnaise, lemon juice, Dijon mustard and celery seeds in a small bowl. Add the dressing to the bowl and stir to coat everything with the dressing.

Season with salt and freshly ground black pepper to taste. Chill until ready to serve.