Cut the top-round steak into 4 pieces. Pound beef with a meat tenderizer until flattened and almost doubled in size. Lightly season the meat on both sides with half of the salt and pepper (1 teaspoon of each for all the meat).
Place flour in a large bowl and add the remaining salt, black pepper, and the cayenne. Taste and adjust seasonings. In another large bowl, mix eggs with milk.
Take a piece of the tenderized beef and coat in flour. Dip the coated beef into the egg mixture and then dip back into the flour again. Repeat for each piece of beef.
In a large skillet, preferably cast-iron, heat 1 inch of oil to 300°F. Take the pieces of coated beef and gently place into the skillet. There will be a lot of popping and hissing, so be careful. After about 3 or 4 minutes, or when the blood starts bubbling out of the top of the steak, with tongs gently turn over the steaks and cook for 5 more minutes.
Remove from skillet and drain on a paper-towel-lined plate. While cooking remaining steaks, you can keep cooked steaks warm in an oven set at 200 degrees.