Prepare the chicken: Pound the chicken halves to an even 1/2-inch thickness. Set aside.
Mix the dry dredge: In a shallow dish, whisk together the flour, cornstarch, salt, pepper, paprika, garlic powder, and cayenne pepper.
Mix the wet dredge: In a second shallow dish, whisk the eggs and buttermilk together.
Coat the chicken: Dip each chicken piece first into the wet mixture, letting excess drip off. Then, press firmly into the dry mixture, ensuring full coverage. For extra crispiness, dip the coated chicken back into the wet mixture briefly, then back into the dry mixture, pressing hard to create craggy bits.
Make the garlic sauce: In a small bowl, combine the mayonnaise, minced garlic, lemon juice, Dijon mustard, and a pinch of salt. Mix well and refrigerate until serving.
Heat the oil: Pour vegetable oil into a deep skillet or Dutch oven to a depth of about 1.5 inches. Heat the oil to 350°F (175°C).
Fry the chicken: Carefully place the coated chicken into the hot oil, ensuring not to overcrowd the pan. Fry for 4 to 6 minutes per side, until golden brown and the internal temperature reaches 165°F (74°C).
Drain: Remove the chicken and place it on a wire rack set over a paper towel-lined baking sheet to drain excess oil. Season lightly with salt immediately after frying.
Toast the buns: Lightly butter the cut sides of the brioche buns and toast them in a dry pan or under the broiler until golden brown.
Assemble the sandwich: Spread a generous amount of the garlic sauce on both halves of the toasted bun. Place lettuce and pickle slices on the bottom bun. Top with a crispy chicken fillet. Place the top bun on the chicken.
Notes
For the crispiest coating, let the fully dredged chicken rest on a wire rack for 10 minutes before frying. This allows the coating to adhere better.
If you prefer not to deep fry, you can air fry the chicken at 380°F (195°C) for 15-20 minutes, flipping halfway, after spraying lightly with cooking oil.
Add a dash of hot sauce to the garlic sauce for a spicy kick.