Special equipment: a 1-gallon resealable freezer bag, 14-inch cast-iron skillet and deep-fry thermometer
For the brine: In a large bowl, combine the bourbon, brown sugar, bay leaves, peppercorns and 1/4 cup salt. Stir to combine. Pour in 4 cups warm water from the tap and stir until the brown sugar dissolves.
Put chicken in a 1-gallon resealable freezer bag and pour in the brine. The chicken should be completely submerged. Seal the bag and refrigerate for 12 to 24 hours.
Pour off the brine and place the chicken on a cooling rack. Pat the chicken dry with paper towels and season with salt and pepper before dredging.
Preheat the oven to 375 degrees F.
For the breading: You will need three medium bowls for the breading. In one bowl, combine 1 cup of the flour with 1/2 teaspoon baking powder. In a second bowl, whisk together the buttermilk, egg and mustard. In a third bowl, combine the remaining 1 1/2 cups flour and 3/4 teaspoon baking powder, along with the cornmeal, garlic powder, cayenne, 1 tablespoon salt and 1 tablespoon pepper.
Follow a basic three step breading process: Dip each chicken breast in the flour (dusting off any excess), then in the buttermilk mixture, and finally in the cornmeal mixture. Dust off any excess before laying each chicken breast on a cooling rack. Allow the chicken to sit out uncovered for 30 minutes. This will make for a crunchier crust.
Set a cooling rack in a rimmed baking sheet. In a 14-inch cast-iron skillet, combine the canola and coconut oils and heat over medium-high heat until the temperature reaches 345 degrees F on a deep-fry thermometer. Working in batches, place the chicken in the skillet bone-side up. The oil should only come halfway up the side of the chicken. Cook until golden brown, about 5 minutes. Carefully flip and cook until golden brown on the other side, 5 to 7 minutes more. If needed, cook on the thicker side of the chicken breast for another minute to crisp the crust. Transfer to the rack as done.
Wipe up any oil drips from the baking sheet so they don't smoke up your kitchen. Transfer the chicken on the rack and baking sheet to the oven and bake until cooked through and the center registers 160 degrees F on an instant-read thermometer, 10 to 20 minutes. Remove from the oven and allow to rest and carry over cooking another 5 degrees F before serving, about 5 minutes.