01 - Preheat grill or oven to 400°F.
02 - Pat chicken completely dry and rub thoroughly with olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper, ensuring even coating on all sides.
03 - Grill chicken 6 to 8 minutes per side or roast on lined baking sheet 20 to 25 minutes until internal temperature reaches 165°F. Let rest 5 minutes before chopping.
04 - Whisk together mayonnaise, apple cider vinegar, lemon juice, horseradish, Dijon mustard, sugar, garlic powder, black pepper, cayenne, and salt in medium bowl until completely smooth and well blended.
05 - Toss shredded cabbage with mayonnaise, apple cider vinegar, salt, and pepper in separate bowl until evenly coated. Refrigerate until ready to assemble.
06 - Cut rested chicken into bite-sized pieces. Transfer to bowl and toss with half the Alabama white sauce until thoroughly coated.
07 - Pile sauced chopped chicken generously onto each toasted bun. Top with generous amount of slaw. Drizzle additional white BBQ sauce over top if desired. Add pickles for extra tang.
08 - Serve sandwiches immediately while chicken and sauce are warm.