Place a 12-inch cast iron skillet over medium-high heat. When the skillet has warmed, add the onions.
Saut� the onions until they become tender (about 10 minutes).
Transfer the onions to a bowl to cool.
Add the next three ingredients (beef through egg white) to the onions, and mix well.
Form four patties using equal portions of the beef mixture. Ensure that each patty is about 3/4-inch thick.
Scatter salt over the skillet's surface making sure there is an equal distribution. Use high heat to cook for a time period of two minutes. Place the patties on the skillet. Cook each face of the patty for five minutes or until done. Serve immediately.
