In a large bowl, whisk together buttermilk, dill pickle juice, egg, and sprinkle of salt and pepper. Immerse chicken in marinade, cover, and refrigerate for at least 2 hours.

In a shallow dish, combine flour, cornstarch, dill weed, baking powder, salt, and pepper. Mix well.

Remove chicken from marinade, let excess drip off, dredge in flour mixture, and coat well. Optionally, dip again in buttermilk followed by another dredge in flour.

Heat oil in a heavy pot to 350°F (175°C). Ensure oil covers chicken halfway.

Lower chicken carefully into the hot oil, fry for 6-8 minutes until golden brown. Flip and fry for another 6-8 minutes until cooked through.

Transfer fried chicken to a wire rack lined with paper towels to drain excess oil.

In a small bowl, combine mayonnaise, lemon juice, garlic, and Dijon mustard. Whisk until smooth. Chill for at least 30 minutes.

Melt butter in a skillet. Toast brioche buns cut-side down for 2-3 minutes until golden brown.

Spread dill aioli on toasted buns, layer lettuce, fried chicken, cheese slice, and pickle chips. Press down gently and serve.