Marinate the chicken overnight. Comes together quickly for dinner, but doubles the next day cold for lunch. Serve with ‘slaw and biscuits.
With kitchen shears and holding chicken on cutting board breast side down, cut off wing tips at first joint. Cut along both sides of backbone. Turn over; flatten with heels of hands. Turn chicken over; with chef’s knife, cut along centre of breast to divide in half. Cut off each leg; at joint, cut into thigh and drumstick pieces. Cut off wings; cut breast diagonally into 2 pieces. Trim all excess fat and loose skin.
Place pieces in 8-inch square glass baking dish. Add onion, thyme sprigs and buttermilk; turn to coat chicken evenly. Cover and marinate in refrigerator for at least 2 hours or for up to 1 day. Remove from marinade, shaking off excess. Set chicken aside on large plate. Discard marinade.
In large bowl, whisk together flour, thyme, salt, cayenne and black pepper. Press chicken, 1 piece at a time, into flour mixture, coating completely. Place on waxed paper–lined baking sheet, keeping pieces separate. Refrigerate for 15 minutes.
Heat 2 large (10- or 12-inch) cast-iron skillets over medium heat. Divide shortening between skillets; heat until pinch of flour mixture dropped in skillet sizzles and browns. Place breast and wings in 1 skillet in single layer, fleshiest side down; place dark meat thighs and drumsticks in the other skillet.
Cover and fry until crisp and brown on bottom, about 9 minutes, adjusting heat as necessary to avoid burning. Turn, cover and fry until crisp and brown on all sides and juices run clear when pierced, about 9 minutes. Drain on paper towel–lined platter.