Combine 1 package salad dressing mix, flour, and pepper, to taste, in a large plastic bag. Set aside. Combine another package salad dressing mix, egg, and 2 cups buttermilk in a shallow bowl. Soak steaks in buttermilk mixture. Remove 1 steak and toss in flour mixture. Shake off any excess flour and dip again in the buttermilk mixture. Return to flour mixture and toss. Repeat process for remaining steaks.
Heat 1/2-inch layer of oil in a large cast iron skillet to 350 degrees F. Place 2 steaks in the pan at a time. Cook for 4 minutes on each side or until golden brown. Drain on paper towels.
To make the gravy, combine 1 cup buttermilk, chicken broth, and gravy package in small saucepan. Bring to simmer over medium heat and stir well. Top steaks with gravy and serve with mashed potatoes and gravy, if desired.