1Heat the oven to 200°F. Pound the steaks to 1/4-inch thick and season with salt and pepper. In a shallow baking dish or pie pan, whisk together the flour and 1 teaspoon salt and a few grinds of pepper. In another shallow baking dish or pie pan, whisk together the eggs and milk. Have ready a baking sheet.
2One at a time, dip the steaks into the flour mixture, then into the egg mixture, and then back into the flour mixture, coating them evenly on both sides. Place on the baking sheet in an even layer.
3In a large heavy frying pan (ideally cast iron), add the oil and heat over medium-high until very hot. Fry the steaks until golden brown and cooked through, turning once, about 4 minutes. While the steaks are fying, clean the baking sheet. Transfer the steaks to the baking sheet and place in the oven to keep warm while you make the gravy.
4Pour off all but 3 tablespoons of the oil from the frying pan. Warm over medium-low heat. Add the flour and and whisk to combine. Let cook, while stirring with a whisk, until the flour mixture begins to brown, about 3 minutes. Slowly whisk in the warm milk, stirring until smooth. Increase the heat to medium and bring to a boil, then reduce the heat to medium-low and simmer, whisking, until thickened, about 3 minutes. Season with salt and pepper. Serve the steaks with the gravy.