Cut the top-round steak into four pieces. Working with one piece at a time, place on a sturdy cutting board or clean countertop, cover with a large piece of plastic wrap, and pound the beef with a meat tenderizer until flattened and almost doubled in size (you want the meat to be about ¼-inch thick). Repeat with the remaining pieces. Sprinkle pieces of beef with salt and black pepper.
In a large, shallow bowl, whisk together the flour, salt, black pepper, and cayenne pepper. In another large, shallow bowl, whisk together the eggs and the buttermilk. Take a piece of the tenderized meat and dip it in the egg mixture. Next, place the meat in the bowl of seasoned flour. Turn to coat it thoroughly. Place the meat back into the egg mixture, turning to coat. Finally, return it back to the flour mixture, ensuring that it is evenly coated on both sides. Place on a clean baking sheet and repeat with the remaining pieces of meat.
In a large, 12-inch cast iron skillet, heat ½ inch of vegetable oil over medium-high heat until a small fleck of flour dropped in the pan sizzles. Carefully place one or two pieces of the meat (whatever fits comfortably without overcrowding) into the skillet. Cook for 3 to 4 minutes, or until the blood starts bubbling out of the top of the steak. Using a pair of tongs, gently turn over the steaks and cook for 5 more minutes. Remove the steaks to a cooling rack to drain while you finish frying the remaining steaks. You can place the cooked steaks in a 200-degree oven to keep warm.
Finally, make the sawmill gravy. (You can start this in another pan while the last piece of steak is cooking.) In a skillet over medium heat, cook the sausage until browned, crumbling it as it cooks. With a slotted spoon, remove the sausage from the skillet and place on a plate. Drain the oil from the pan, reserving 2 tablespoons in the skillet (if your sausage didn't yield enough drippings, you can use vegetable oil to get to the 2 tablespoons). Sprinkle the flour over the drippings, and whisk together, cooking for about 2 minutes, until a dark roux is formed. Add the milk slowly to the skillet, whisking continuously. Reduce the heat to medium-low and continue whisking until the mixture is thickened, about 2 more minutes. Remove from the heat, stir in the reserved sausage, and season to taste with salt and black pepper. (If the gravy is too thick, you can thin it by whisking in more milk, a tablespoon at a time.)
Serve the steaks with the sawmill gravy poured over top.
Note: You can purchase cube steak, which is already-tenderized cuts of round steak, and omit step 1 up until the last line - be sure to still season with salt and pepper!