Pour 1 inch of oil in large cast iron skillet. Heat oil in skillet over medium heat on stove top while preparing meat.
Place flour in a shallow dish. Season with salt and pepper and stir to mix well.
Beat egg and milk together. Pour into another shallow dish.
Place milk mixture and flour next to one another to create a "dredging station."
Cut cube steak into 1 inch strips. Salt and pepper both sides of each strip. Place the strip into the flour, coating both sides. Then place the strip into the egg mixture, coating both sides. Coat strip with flour once more. Gently shake off extra.
When oil is hot (sprinkle a few drops of flour in, it should sizzle), carefully place strips side by side in skillet. Using tongs or a fork, turn strips once when bottoms begin to brown, (about 1-2 minute on each side).
When browned on both sides, remove strips from skillet and place on a paper towel lined rack to drain any excess oil.