To make Chicken Fried Steak: Heat a deep, heavy skillet with at least 1/2-inch of oil to 340 degrees F. Alternatively, heat oil in a deep fryer to 340 degrees F.

Cut steak into 1/2-inch thick slices to make 6 (6-ounce) portions and remove any fat or gristle. Pound it with the coarse side of a tenderizing mallet until it is double in size and half as thick. In a shallow bowl, make an egg wash by combining the eggs and milk. In another shallow bowl or pan, make a seasoned breading by combining the flour, salt, and pepper. Dredge the steak in the seasoned flour, dip it in the egg wash, and then return it to the flour and push the flour into the steak with your fingers so that there are no moist spots. Immediately slide the steak into the hot oil, in batches as necessary to prevent overcrowding, and fry on 1 side until golden and crispy; then turn over and cook the rest of the way. The steaks are done when you lift them with a pair of tongs and they are stiff, not floppy. Keep warm while making the gravy.

To make Cream Gravy: Mix the canola oil and flour in a saucepan and cook this roux over medium heat until it looks grainy and becomes slightly golden in color, just a couple of minutes. Remove from heat. Add pepper and salt and mix well. Add milk, return the pan to the heat, and increase heat to high. Whisk until mixture comes to a boil and thickens. Add hot water to thin, if gravy is too thick. Remove from heat to prevent scorching. The gravy should be as thick as pancake batter. Pour over chicken fried steak and serve.