To prepare the chicken, place boneless, skinless chicken breasts in a saucepan and cover them with cold water or low-sodium chicken broth. Enhance the flavor by adding a bay leaf, a few peppercorns, and a pinch of salt.
Bring the liquid to a gentle simmer over medium heat, then immediately reduce the heat to low, cover the pan, and cook for 15-20 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Remove the chicken from the liquid and let it cool slightly. Once cool enough to handle, use two forks to shred the chicken into bite-sized pieces, or dice it into small, uniform cubes.
Finely dice celery and red onion (or sweet onion) into small, uniform pieces, aiming for pieces no larger than a quarter-inch.
For the pecans, spread them in a single layer on a baking sheet or in a dry skillet over medium heat. Toast for 5-7 minutes in the oven (at 300°F/150°C) or 3-5 minutes on the stovetop, stirring frequently, until fragrant and lightly golden. Allow them to cool completely before coarsely chopping.
In a large mixing bowl, combine the prepared chicken, finely diced celery, and diced onion.
Add your chosen mayonnaise (ideally Duke's for that authentic tang), Dijon mustard, a generous pinch of salt, and freshly ground black pepper. Start with about half the suggested mayonnaise quantity and add more if needed to reach your desired level of creaminess.
Gently fold all the ingredients together until the chicken and vegetables are evenly coated with the rich, creamy dressing.
Finally, carefully fold in the cooled, coarsely chopped toasted pecans, ensuring they are distributed throughout the salad for that essential crunch.
Taste and adjust the seasonings as needed. You might want a little more salt, pepper, or another touch of Dijon mustard to enhance the tang and overall flavor profile.
For the absolute best results, cover the bowl and refrigerate the chicken salad for at least 30 minutes to allow the flavors to meld beautifully.