Place the halved chicken breasts in a bowl. Pour buttermilk, hot sauce, salt, and pepper over the chicken. Cover and refrigerate for at least 4 hours, or preferably overnight.
In a shallow dish, whisk together the flour, cornstarch, paprika, garlic powder, and cayenne pepper. This is your dry dredge mix.
Remove chicken from the buttermilk, letting excess drip off, but do not pat dry.
Dredge each piece of chicken thoroughly in the dry mix, pressing the flour onto the chicken to create a thick coating.
For extra crispiness, dip the floured chicken back into the leftover buttermilk mixture for just a second, then immediately return it to the dry dredge mix. Press firmly again to build a thick, craggy crust.
Heat 2 inches of vegetable oil in a deep skillet or Dutch oven to 350°F (175°C).
Carefully place the coated chicken into the hot oil, ensuring not to overcrowd the pan. 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 wire rack set over a baking sheet to drain excess oil. Sprinkle lightly with salt immediately after removing from the oil.
Lightly toast the brioche buns.
Assemble the sandwich: Spread mayonnaise on both halves of the bun, place the crispy chicken fillet on the bottom bun, top with pickle slices, and place the top bun on. Serve immediately.
Notes
For the best crust, use chicken thighs instead of breasts; they stay juicier.
To prevent sogginess, do not let the dredged chicken sit before frying; cook it immediately after the second dredge.
If you prefer baking, spray the dredged chicken with cooking spray and bake at 400°F (200°C) for 20-25 minutes, flipping halfway.