Stir together 2 tablespoons olive oil, 1 tablespoon salt, paprika, thyme, 1 teaspoon black pepper, and cayenne in a small bowl. Rub mixture on outside and under skin of chicken. Stuff cavity with lemon, garlic cloves, and 4 onion quarters.

Place 2 inverted shallow ramekins in a 6-quart slow cooker. Place carrots, celery, and remaining onion quarters around ramekins; pour water over vegetables. Place chicken, breast side up, on top of ramekins. Cover and cook on HIGH until a thermometer inserted into thickest portion of breast registers 165°F, about 3 1/2 hours. Transfer chicken to a cutting board, and let rest 15 minutes.

Preheat broiler to HIGH with oven rack 6 inches from heat. Remove ramekins, and pour stock mixture through a wire-mesh strainer into a bowl; discard solids. Reserve stock for later use. Cut chicken into 6 pieces, and place, skin side up, on an aluminum foil-lined rimmed baking sheet. Broil until skin is golden brown and crispy, 4 to 6 minutes. Set chicken aside

Whisk together mayonnaise, apple cider vinegar, 1/2 teaspoon black pepper, hot sauce, Worcestershire sauce, 1/4 teaspoon salt, garlic powder, and sugar in a large bowl. Add 12 oz. shredded, skinless Chicken; toss to coat.

Combine red cabbage, scallions, 2 teaspoon olive oil, and 1/4 teaspoon kosher salt. Top bottom halves of biscuits evenly with chicken mixture and red cabbage mixture. Top each with 3 sweet-hot pickle slices, and cover with biscuit tops.