01 - Preheat grill or stovetop grill pan over medium-high heat.
02 - Rub chicken breasts with olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper, ensuring even coverage on all sides.
03 - Place seasoned chicken on the preheated grill. Cook for 6 to 8 minutes per side, or until fully cooked through to an internal temperature of 165°F. Remove from heat and let rest for 5 minutes before chopping.
04 - While chicken rests, whisk together mayonnaise, apple cider vinegar, lemon juice, prepared horseradish, Dijon mustard, sugar, garlic powder, black pepper, and cayenne pepper in a medium bowl until smooth and well combined. Taste and adjust salt and vinegar as needed.
05 - Using a sharp knife, chop the rested chicken into bite-sized pieces. Transfer to a mixing bowl and toss generously with the prepared Alabama white BBQ sauce, reserving a small amount for drizzling if desired.
06 - Lightly toast the sandwich buns on the grill or in a toaster for added texture and to prevent sogginess.
07 - Pile the sauced chopped BBQ chicken onto the bottom halves of the toasted buns. Top each sandwich with a generous spoonful of coleslaw and sliced pickles if using.
08 - Drizzle any reserved white BBQ sauce over the toppings, close with the bun tops, and serve immediately while warm.