Sautee the finely chopped onion in the olive oil. Sautee until the onion is soft, translucent and starts to carmelize. Then take off of heat to cool.
Place ground beef in a large bowl and season with Salt, Pepper and Garlic Salt. Pour in the carmelized onions and mix into the meat with your hands, making sure the onion is disbursed evenly.
Seperate the meat into 4 patties, roll into balls and flatten. Season the outside of the meat with some salt and pepper. They are ready for the grill, place on a BBQ grill till cooked as desired. Place the cheese on the patties to melt 1 minute before the meat is done.
Fry the eggs in the margarine individually. Once they are cooked sunny side up, flip them to cook over easy. You want the yoke to just be lightly cooked solid, not runny and not hard.
Assemble the burgers with the veggies on the bottom, the patty with cheese and then the egg. The egg tastes much better next to the cheese and meat then on the veggies. Enjoy!