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.
03 - Grill chicken for 6-8 minutes per side, or until fully cooked (internal temperature reaches 165°F). Remove and let rest for 5 minutes.
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 bowl until smooth. Adjust salt and vinegar to taste.
05 - Chop the cooked chicken into bite-sized pieces. Transfer to a bowl and toss generously with the Alabama white BBQ sauce, reserving a small amount for drizzling if desired.
06 - Toast sandwich buns lightly on the grill or in a toaster, if desired.
07 - Pile chopped BBQ chicken onto the bottoms of buns. Top each with a generous spoonful of coleslaw and sliced pickles.
08 - Drizzle with extra BBQ sauce, close sandwiches, and serve immediately.