Season the chicken generously with salt and black pepper; place on a baking sheet, cover loosely with plastic wrap and refrigerate 1 hour.
Mix the buttermilk, hot sauce, bay leaf, garlic and thyme in a large resealable plastic bag. Add the chicken, making sure the pieces are submerged. Seal and refrigerate 2 to 4 hours.
Mix the flour, baking powder, paprika, onion powder, cayenne, 3 1/2 teaspoons salt and 1 1/2 teaspoons black pepper in a separate resealable bag.
Fill a deep 12-inch cast-iron skillet halfway with equal parts peanut oil and shortening. Heat over medium heat until a deep-fry thermometer registers 350 degrees F.
Remove about half of the chicken pieces from the buttermilk mixture, letting the excess drip off. Transfer to the bag of seasoned flour; seal and shake to thoroughly coat. Remove from the bag, shake off any excess flour and transfer to a rack.
Carefully lower the coated chicken into the oil. The temperature will drop to 300 degrees F to 325 degrees F; adjust the heat to maintain this temperature so the crust doesn't burn before the meat is cooked. Fry, undisturbed, 2 to 3 minutes to set the crust, then carefully lift with tongs to check the browning; continue to fry, turning as needed, until golden brown and cooked through, 12 to 14 more minutes for smaller pieces and 14 to 16 more minutes for larger ones. (A thermometer should register 160 degrees F in the breasts and 170 degrees F in the thighs and drumsticks.)
Remove the chicken to a clean rack to drain, sprinkle with salt and let rest a few minutes. Repeat with the remaining chicken. Serve hot or at room temperature.
Photograph by Yunhee Kim
Recipe courtesy Food Network Magazine