In another bowl, mix the flour with salt and pepper.
Dip each steak into the egg mixture, then dredge in the flour mixture, ensuring each steak is well-coated.
Heat the cooking oil in a large skillet over medium-high heat.
Fry each steak until golden brown, about 3-4 minutes on each side.
Remove from the skillet and let rest on a wire rack.
For the gravy, remove most of the oil from the skillet, leaving about 2 tablespoons. Add 2 tablespoons of the used flour mixture, stir and cook for a minute. Slowly whisk in the remaining milk. Cook until thickened, season with salt and pepper.
Serve the steak warm, smothered in gravy.
Notes
Make sure the oil is hot enough before frying. You can test this by dropping a tiny bit of flour into the oil; if it sizzles, it's ready.
Don't overcrowd the pan. Fry one or two steaks at a time to ensure even cooking.
After frying, let the steaks rest on a wire rack over a baking sheet. This keeps them crispy.
For a creamier gravy, you can add a touch of heavy cream.
Season every layer, from the steaks themselves to the flour mixture, for the best flavor.