Cut each chicken breast into 3- x 1-inch strips, and set aside.
Combine flour and next 3 ingredients in a large shallow dish.
Whisk together buttermilk, 3/4 cup barbecue sauce, and eggs in a bowl. Dredge chicken pieces in flour mixture; dip in buttermilk mixture, and dredge again in flour mixture. (If flour gets gummy, just press into chicken pieces.)
Pour oil to a depth of 1 1/2 inches in a deep skillet or Dutch oven; heat to 360°.
Fry chicken, in batches, 5 to 7 minutes or until golden. Drain on wire racks over paper towels. Serve with extra barbecue sauce.
Barbecue-Battered Pork Chops: Substitute 3 pounds boneless breakfast pork chops for chicken, and proceed as directed. For a delicious serving idea, serve cooked chops in biscuits.