Heat 6 cups of water mixed with 2 tablespoons of salt in a Dutch oven over medium heat. Place the chicken in the water and heat until the water heats to 170 degrees. Turn off the heat, cover the pot, and let stand until the temperature of the chicken is 165 degrees, about 15 minutes.
Remove the chicken from the water and place on paper towels to drain. Refrigerate until chicken is cool, about 30 minutes.
Meanwhile, whisk together the mayonnaise, lemon juice, Dijon mustard, spicy brown mustard, celery, onion, and fresh herbs in a medium sized mixing bowl. Add salt and pepper to taste.
Cut the chicken into small pieces or shred and add to the mayonnaise mixture. Mix well. Season with salt and pepper to taste.
Serve immediately or refrigerate for up to 3 days.