Pulled chicken: add all of the slow cooker pulled chicken ingredients to a slow cooker or crockpot on low for 5 to 6 hours.
After the time is up, turn off the slow cooker, remove the lid, and allow everything to cool for 30 minutes. Then remove the chicken to a cutting board and shred it into smaller pieces with two forks. Place all of the shredded chicken back into the slow cooker with the remaining liquid and allow it to absorb broth for another 15 minutes.
Move the chicken and as much of the broth as you'd like to save into a sealed container and place it in the refrigerator for up to 5 days. You can use this chicken for chicken salad, tacos, and obviously, things like this sandwich.
Alabama white sauce: add mayonnaise, apple cider vinegar, ground black pepper, garlic powder, sugar, prepared horseradish, salt, and lemon juice to a medium-sized bowl and whisk until fully combined. Add a pinch of cayenne pepper powder if you would like to add a little spice to the sauce.
Add your Alabama white sauce to a sealed container and store it in the refrigerator for around a week or so.
Sandwich assembly: this sandwich works best with a toasted bun. It's optional, but you should do it. Toast a bun, and while you're toasting it, if you want to add cheese to the sandwich, place it on the top or bottom slice of the bun after you toast it and let the cheese melt a little.
Heat up a sandwich-sized amount of chicken with a couple of teaspoons of the broth in the container in a small pan over medium heat for about 3 or 4 minutes or until the meat is warmed through. Turn off the pan and add some spoonfuls of Alabama white sauce on top of the meat and stir everything around to coat the meat well.
Place the sauced-up meat on top of the bottom sandwich bun and top with pickles and red onion (optional). Also, this is a good time to add more sauce if desired.
Close the sandwich and serve