Slice the meat into thin "patty" pieces. You can cook the steak first, then slice it if you use it for your sandwich.
Use Worcestershire sauce, salt, pepper, and garlic powder to season the steak on both sides.
Melt the butter in a skillet over medium heat and saute the onions until caramelized.
Add the steak to the skillet and melt a tablespoon of the butter over medium-high heat. Cook until well done, a few minutes on each side. Remove from the pan and set aside.
Crack eggs into a skillet after heating butter in a nonstick pan or griddle over medium-low heat. Cook the eggs to your preferred doneness.
Spread a little butter on a freshly toasted bagel if preferred. Add a slice of cheese to the bottom of each bagel. Add the steak to the bottom bagel, then top with fried onions, an egg, and cheese.
Close the sandwiches with the bagel tops and serve warm.