Pound the chicken halves to an even 1/2-inch thickness. Place the chicken in a bowl, cover with buttermilk and hot sauce, and marinate in the refrigerator for at least 4 hours or overnight.
In a shallow dish, whisk together the flour, cornstarch, salt, pepper, paprika, garlic powder, and cayenne pepper.
Remove chicken from the marinade, letting excess drip off. Dredge each piece thoroughly in the flour mixture, pressing firmly to coat.
Heat about 2 inches of vegetable oil in a deep skillet or Dutch oven to 325°F (160°C).
Fry the chicken in batches for 5 to 6 minutes until lightly golden. Remove and place on a wire rack. Increase oil temperature to 375°F (190°C).
Return the chicken to the hot oil and fry a second time for 2 to 3 minutes until deep golden brown and extremely crispy. Drain on a clean wire rack.
While the chicken rests, prepare the sauce: Combine mayonnaise, minced garlic, lemon juice, Dijon mustard, salt, and pepper in a small bowl. Mix well.
Lightly butter the cut sides of the brioche buns and toast them in a dry pan over medium heat until golden brown.
Assemble the sandwich: Spread a generous amount of garlic sauce on both the top and bottom buns. Place one crispy chicken fillet on the bottom bun. Add any desired toppings like pickles or lettuce. Place the top bun on the sandwich.
Notes
For the crispiest result, ensure the oil temperature is correct for the second fry; this cooks the crust quickly without overcooking the chicken.
You can substitute mayonnaise with Greek yogurt for a slightly lighter garlic sauce base.
Use a meat thermometer to check the internal temperature of the chicken; it should reach 165°F (74°C).