For the steak: Begin with setting up an assembly line of dishes. Mix the milk with the eggs in one; mix the flour with the seasoned salt, paprika, cayenne and 1 1/2 teaspoons black pepper in another; and put the meat in a third. Then have 1 clean plate at the end to receive the breaded meat.
Work with 1 piece of meat at a time. Sprinkle both sides with salt and black pepper, then place it in the flour mixture. Turn to coat. Place the meat into the milk/egg mixture, turning to coat. Finally, place it back in the flour mixture and turn to coat (dry mixture/wet mixture/dry mixture). Place the breaded meat on the clean plate, then repeat with the remaining meat.
Heat the oil in a large skillet over medium heat. Add the butter. Drop in a few sprinkles of flour to make sure it's sufficiently hot. When the butter sizzles immediately, you know it's ready. (It should not brown right away; if it does, the fire is too hot.) Cook the meat 3 pieces at a time until the edges start to look golden brown, about 2 minutes each side. Remove the meat to a paper towel-lined plate and keep warm by covering lightly with another plate or a sheet of foil. Repeat until all the meat is cooked.
For the gravy: Put the skillet with the grease back over the heat. When the grease is hot, sprinkle the flour evenly over the grease. Using a whisk, mix the flour with the grease, creating a golden-brown paste. Add more flour if it looks overly greasy; add a little more grease if it becomes too pasty/clumpy. Keep cooking until the roux reaches a golden brown color, about 5 minutes.
Pour in 3 cups of the milk, whisking constantly. Add the seasoned salt and black pepper to taste and cook, whisking, until the gravy is smooth and thick, 5 to 10 minutes. Be prepared to add more of the remaining milk if it becomes overly thick. Be sure to taste to make sure the gravy is sufficiently seasoned.
Serve the steaks with the gravy.