Place chicken halves in a bowl. Combine buttermilk, hot sauce, salt, and pepper. Pour over chicken, cover, and refrigerate for at least 4 hours or overnight.
Prepare the dredging station: Place flour in one shallow dish, beaten eggs in a second, and a mix of Panko breadcrumbs and 1/2 cup Parmesan cheese in a third.
Remove chicken from the brine, letting excess drip off. Dredge each piece first in flour, shaking off excess. Dip into the egg mixture. Finally, press firmly into the Panko mixture to coat completely.
Heat about 1.5 inches of oil in a heavy-bottomed skillet to 350°F (175°C).
Carefully place chicken into the hot oil, ensuring not to overcrowd the pan. Fry for 4 to 6 minutes per side until golden brown and cooked through (internal temperature reaches 165°F or 74°C). Remove and drain on a wire rack.
While chicken fries, make the sauce: In a small saucepan, melt the butter over medium heat. Add minced garlic and cook until fragrant, about 1 minute. Do not brown the garlic.
Remove the pan from the heat. Whisk in the mayonnaise, 1/4 cup Parmesan cheese, lemon juice, and parsley. Mix until smooth.
Lightly toast the brioche buns. Brush the cut sides of the toasted buns with a small amount of the garlic parmesan sauce.
Brush the hot, crispy chicken fillets generously with the remaining garlic parmesan sauce.
Assemble the sandwich: Place the sauced chicken on the bottom bun, top with pickles, and place the top bun on. Serve immediately.
Notes
For extra crispiness, you can double dredge the chicken by dipping it back into the egg and Panko mixture after the first coating.
If you prefer baking, place coated chicken on a wire rack over a baking sheet and bake at 400°F (200°C) for 20-25 minutes, flipping halfway.
For an air fryer method, cook at 380°F (195°C) for 12-15 minutes, flipping halfway.
Substitute brioche buns with potato rolls for a softer texture.