Pulled Chicken Sandwich with White Sauce

• 1 (3-4 lb) whole chicken
• 1/2 cup BBQ sauce
• hamburger bun

Apple Cider Injection:

• 3/4 cup apple cider
• 1/4 cup unsalted butter , melted
• 1 teaspoon garlic powder
• 1/4 teaspoon salt

Sweet Rub:

• 2 tablespoon brown sugar
• 1.5 tablespoon sea salt
• 1 teaspoon black pepper
• 1 teaspoon smoked paprika
• 1 teaspoon garlic powder
• 1 teaspoon onion powder
• 1.5 teaspoon ground mustard
• 1/2 teaspoon dried thyme
• 1 teaspoon cayenne pepper

White Sauce:

• 2 cups mayonnaise
• 1/2 cup apple cider vinegar
• 1/2 cup prepared horseradish
• 1 tbsp lemon juice