Nashville Hot Chicken Sandwich

Ingredients

• 1/4 cup mayonnaise
• 2 tablespoons apple cider vinegar
• 2 teaspoons granulated sugar
• Kosher salt
• freshly ground black pepper
• 1/2 head red cabbage, cored, thinly sliced (about 4 cups)
• 1 cup shredded carrots
• 1 shallot, thinly sliced
• Vegetable oil, for frying
• Miss Brown's House Seasoning, recipe follows
• 2 skin-on, boneless chicken breasts (about 12 ounces each), cut in half crosswise (see Cook's Note)
• 1 1/2 cups all-purpose flour
• 2 cups buttermilk
• 1/2 cup hot sauce, such as Frank's RedHot
• 4 split potato rolls, toasted, for serving
• Dill pickles, for serving
• 1 stick (8 tablespoons) unsalted butter
• 1 cup hot sauce, such as Frank's RedHot
• 1/4 cup packed light brown sugar
• 1/4 teaspoon cayenne
• 1 teaspoon Miss Brown's House Seasoning, recipe follows
• 1 teaspoon onion powder
• 1 teaspoon sweet paprika
• 1 teaspoon garlic powder
• 1 teaspoon kosher salt
• 1 teaspoon freshly ground black pepper