Heat the oil over medium high in a large heavy-bottomed stainless skillet.
In a medium sized bowl, combine the ground chuck, chopped onion, egg, hot sauce, seasoned salt, garlic powder and pepper. Shape into 4 to 6 equal sized patties.
Dip each patty into the flour and cook until browned on both sides; remove and set those aside.
Add the sliced onions to the skillet and cook over medium heat until lightly caramelized, stirring regularly.
Whisk together the beef broth and water with 1/4 cup of flour, 1/2 teaspoon of seasoned salt and pepper to taste until well combined. Pour into the skillet with the onions and stir constantly, until mixture begins to thicken.
Return the hamburger steaks to the skillet, turn to coat, add sliced mushrooms if using, and reduce heat to simmer. Cook, covered, for about 20 minutes longer.
Cook's Note: The brown gravy for these patties is pretty good on its own since it's made from the pan drippings. But if you have some Kitchen Bouquet, just a splash of it adds a bit more depth and is delicious. If you find that you need a binder, add in some fresh bread crumbs to the ground beef. If using pre-made hamburger steak patties, omit the onion, egg and hot sauce, and sprinkle both sides of the patties with the seasoned salt, garlic powder and pepper, pressing in the seasoning a bit. Then dip each patty in the flour and proceed with the remaining recipe.