Transfer the brine to a large bowl and add the chicken along with enough cold water to completely submerge the chicken. Cover and refrigerate for at least 3 hours and up to overnight. (The longer you brine the chicken, the more intense the pickle flavor and the saltiness.)
When you're ready to fry the chicken, preheat the oven to 200°F (93°C). Remove the chicken from the brine and rinse it under cool water to remove any salt, seeds, or dill clinging to it.
Place the buttermilk in a large bowl, add the chicken, and turn to coat.
Place the flour, sea salt, black pepper and cayenne pepper in a separate large, shallow bowl or plastic bag and stir or shake to mix.If you prefer a thin batter coating on your fried chicken, use a bag to shake the flour mixture with the chicken. If you prefer a thick batter coating on your fried chicken, use a bowl and your hands to dredge the chicken in the flour mixture. Pour enough oil into a large cast-iron skillet or Dutch oven to reach a depth of at least 1/4 inch. The oil should reach about 1/3 of the way up the side of the skillet and be deep enough to submerge the chicken about halfway (bear in mind that the level of the oil will rise slightly when you add the chicken). Place the skillet over medium-high heat until the temperature reaches between 360°F and 375°F (182°C and 191°C) on an instant-read thermometer.
Working in small batches, remove the chicken from the buttermilk, one piece at a time, and dredge or shake it in the flour mixture, turning to coat it evenly on all sides, beginning with the large pieces. Shake off any excess flour.
Still working in small batches, place the chicken in the hot oil and fry, turning once, until golden brown and cooked through and the breast meat registers 165°F (74°C) on an instant-read thermometer, 5 to 7 minutes per side. Do not overcrowd the skillet or the chicken will not fry evenly. If the chicken seems as if it's browning too quickly, reduce the heat or use tongs to turn the pieces on their skinny sides. Bring the oil back up to temperature before starting the next batch.
Transfer the fried chicken to a wire rack situated on a rimmed baking sheet to drain. Season with additional salt and pepper to taste, if desired (you'll want to go easy on the salt since there's a lot of it in the brine) and keep the chicken in the warm oven while the next batch is frying.
While the chicken is cooking, combine the Sriracha and honey in a small bowl and stir to combine. Taste and, if necessary, add a smidgen more of either ingredient according to personal preference. Serve the chicken hot or at room temperature with the Sriracha honey on the side for drizzling or dipping.