Place the chicken pieces in a bowl. Pour buttermilk and hot sauce over the chicken. Let it marinate for at least 30 minutes, or up to 4 hours in the refrigerator.
In a shallow dish, whisk together the flour, cornstarch, paprika, garlic powder, salt, and pepper for the dry dredge.
Remove chicken from the buttermilk, letting excess drip off. Dredge the chicken thoroughly in the flour mixture, pressing firmly to coat.
Dip the floured chicken back into the buttermilk mixture briefly, then immediately return it to the dry dredge. Press the flour onto the chicken again to create a thick, craggy coating. Set aside on a wire rack.
Prepare the slaw: In a medium bowl, combine the shredded cabbage and carrot.
In a small bowl, whisk together the mayonnaise, apple cider vinegar, sugar, Dijon mustard, salt, and pepper until smooth.
Pour the dressing over the cabbage mixture and toss well to coat. Refrigerate for at least 15 minutes to allow flavors to meld.
Heat about 2 inches of vegetable oil in a deep, heavy-bottomed pot or Dutch oven to 350°F (175°C).
Carefully place chicken pieces into the hot oil, ensuring you do not overcrowd the pot. Fry for 5 to 7 minutes per side, until golden brown and the internal temperature reaches 165°F (74°C).
Remove the chicken and place it on a clean wire rack set over a baking sheet to drain excess oil. Season immediately with a pinch of salt.
Lightly butter the cut sides of the brioche buns and toast them in a skillet over medium heat until golden brown.
Assemble the sandwich: Place a crispy chicken fillet on the bottom bun. Top generously with the creamy coleslaw. Place the top bun on the slaw. Serve immediately.
Notes
For extra spice, add cayenne pepper to the dry dredge mixture.
If you prefer a less tangy slaw, reduce the apple cider vinegar by one teaspoon.
Use a meat thermometer to confirm the chicken is fully cooked for food safety.