Fill a 12-inch pan (with a lid) 3/4 of the way with water and bring to a simmer. Add the garlic head, celery tops and bottoms, onion tops and bottoms, bay leaves, 1 teaspoon of salt, and 1/2 teaspoon of pepper. Return the liquid to a simmer.
Rinse the chicken briefly under cool running water, and then pat dry with paper towels. Season the chicken on both sides with the remaining salt and pepper. Add the chicken breasts to the poaching liquid, cover, and cook until the internal temperature reaches 165 degrees F when tested with an instant-read thermometer, about 20 to 25 minutes. Remove the chicken breasts and set aside to cool.
While the chicken is cooking, combine the minced garlic, diced celery, finely chopped red onion, mayonnaise, mustard, and herbs in a large mixing bowl and mix well.
When the chicken is cool enough to handle, cut it into 1/2-inch dice, add the chicken and the pecans to the mayonnaise mixture, and mix well. Serve the salad immediately, or transfer to the refrigerator to chill.