Preheat the oven to 200°F.

Flatten the round steak pieces to 1/4-inch thickness using a meat mallet.

In a large bowl, combine flour, 1/2 teaspoon salt, 1 teaspoon black pepper, and cayenne.

In another bowl, whisk together eggs and buttermilk.

Pour vegetable oil into a large cast-iron skillet, filling halfway up the side.

Heat the oil over medium heat.

Dredge each steak piece in the flour mixture, shaking off excess.

Dip the floured steak into the egg mixture, letting excess drip off.

Redredge the steak in the flour mixture, coating both sides.

Place the dredged steak on a sheet pan and repeat with remaining pieces.

When the oil is hot, add as many steak pieces as fit in a single layer (usually two).

Cook until golden brown on the bottom, about 4 minutes.

Flip and cook until golden brown on the other side, about 4 minutes.

Transfer the fried steaks to a wire rack on a sheet pan and place in the oven to keep warm.

Repeat the frying process with the remaining steak pieces.

Remove all but 2 tablespoons of oil from the skillet.

Heat the remaining oil over medium heat and add 2 tablespoons of flour from the dredging process.

Stir constantly with a whisk until the roux turns a dark brown color.

Reduce heat to low and slowly stir in the milk, making sure to eliminate any clumps of flour.

Season with salt and plenty of pepper and cook until slightly thickened, ensuring it coats the back of a spoon.

Add more milk or water to thin if needed.

Serve the chicken-fried steak topped with the cream gravy.