Batter: Combine beaten egg, milk, chicken broth, salt and pepper in a medium bowl. Whisk to combine. add 3/4 cup self-rising flour and cornstarch, whisking until smooth. Let batter rest 5 -10 minutes.
Cook Chicken: Heat shortening or oil in fryer to 350 degrees F. Coat chicken pieces with dry flour, then dip chicken into batter. Allow excess batter to drip off, then place 3 pieces of battered chicken into the hot oil and fry for 6 to 8 minutes or until browned. Drain fried chicken strips on paper towels.