Set up a breading station: place 1 cup of flour in a shallow bowl. In another shallow bowl, whisk together the eggs and 1/2 cup of milk until well blended.

Season the cube steaks with 1 teaspoon of the salt and 3/4 teaspoon of the pepper. Dredge each steak in the flour, shaking off excess, then dip into the egg mixture, and coat once more in the flour, pressing to adhere and making sure the edges are well covered.

Heat 1/4 inch of oil in a large heavy skillet over medium heat. Fry the steaks for 4 to 6 minutes per side until golden brown and the internal temperature reaches 160°F. Drain on paper towels and keep warm.

Drain the oil from the skillet, leaving 2 tablespoons of drippings. Stir in the remaining 1/4 cup flour, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Cook and stir for 3 to 4 minutes until golden.

Gradually whisk in 1 cup of water and the remaining 1 cup of milk. Bring to a boil, stirring constantly, until the gravy thickens, 1 to 2 minutes. Season to taste and pour generously over the fried steaks.