Place the chicken pieces in a bowl and cover them with buttermilk, salt, and pepper. Let the chicken marinate in the refrigerator for at least 1 hour, or up to 4 hours.
In a shallow dish, whisk together the flour, cornstarch, paprika, and garlic powder. This is your dry dredge.
Remove one piece of chicken from the buttermilk, letting excess drip off. Dredge the chicken thoroughly in the flour mixture, pressing firmly to coat all sides. Shake off any excess flour.
Heat about 2 inches of vegetable oil in a deep skillet or Dutch oven to 325°F (160°C).
Carefully place the dredged chicken into the hot oil, ensuring not to overcrowd the pan. Fry for 6 to 8 minutes, turning occasionally, until the internal temperature reaches 165°F (74°C) and the crust is deep golden brown and crisp.
Remove the chicken and place it on a wire rack set over a baking sheet to drain excess oil. Do not place it directly on paper towels, as this can steam the bottom and make it soggy.
While the chicken rests, prepare the sauce: In a small saucepan, combine the honey, hot sauce, apple cider vinegar, and cayenne pepper. Heat over low heat until just warm and fully mixed. Do not boil.
Lightly butter the cut sides of the brioche buns and toast them in a dry pan or under the broiler until golden brown.
Brush the hot, crispy chicken pieces generously on both sides with the spicy honey sauce.
Assemble the sandwich: Place the sauced chicken on the bottom bun. Top with dill pickle chips and shredded lettuce. Place the top bun on the sandwich. Serve immediately.
Notes
For extra crispiness, you can double-dredge the chicken: dip the floured chicken back into the buttermilk briefly, then back into the flour mixture again before frying.
Toasting the bun prevents it from absorbing moisture from the chicken and sauce.
If you prefer baking, place the dredged chicken on a wire rack over a baking sheet and bake at 400°F (200°C) for 20-25 minutes, flipping halfway, until cooked through. Brush with sauce after baking.