How to Make It
In a large, deep bowl, combine the water with 1/3 cup of the salt, the brown sugar, garlic, thyme sprigs and black peppercorns and stir to dissolve the salt. Add the chicken pieces, submerging them in the brine. Refrigerate the chicken overnight.
Preheat the oven to 300°. In a large, heavy pot, heat 2 inches of oil to 325°. Drain the chicken and pat dry with paper towels.
In a large bowl, combine the flour, baking powder, cornstarch, black pepper, cayenne and the remaining 1 teaspoon of salt. Set a rack over a large rimmed baking sheet near the stove. Dredge half of the chicken pieces in the spiced flour, then shake off the excess. Fry the chicken pieces for about 10 minutes, or until an instant-read thermometer inserted into the thickest part of a thigh registers 160°. Reduce the heat if the chicken browns too quickly. Transfer the chicken pieces to the rack and keep them warm in the preheated oven while you coat and fry the remaining chicken pieces. Serve the fried chicken hot.