Recipe adapted from Sara Foster's Southern Kitchen (Random House; 2011).
Place chicken in a large bowl and cover with cold water. Add 2 tablespoons salt, the sugar, vinegar, and bay leaves and stir until salt and sugar dissolve. Cover and refrigerate overnight.
Place buttermilk in a large, shallow bowl. Lift chicken from brine and transfer to buttermilk. In another large, shallow bowl or zip-top bag, stir or shake together flour, 1 tablespoon salt, 1/2 teaspoon pepper, and pinch of cayenne to combine.
Line a platter with a brown paper bag and place near stove. In a large cast-iron skillet, heat shortening over medium-high until a deep-fry thermometer reads 350 degrees to 375 degrees (a small cube of bread should brown in less than 1 minute). Oil should be deep enough to come halfway up sides of chicken; the level will rise slightly when chicken is added. Beginning with larger pieces, lift chicken from buttermilk, letting excess drip off, and dredge or shake in flour mixture until evenly coated. Shake off excess.
Working in batches, add chicken, skin side down, to pan (do not crowd pan); reduce heat to medium. Fry until golden brown on both sides and juices run clear when thigh is pierced with a knife (an instant-read thermometer inserted into thickest part of thigh, avoiding bone, should read 165 degrees), 10 to 12 minutes per side.
Transfer chicken to platter to drain. Season with salt and pepper and let sit 10 minutes. Serve warm or at room temperature.