Start by making the carmelized onions. Thinly slice the onion. Melt butter in a large saute pan, over medium high heat. Add the onions, and stir so melted butter coats onions. Cover the pan, and tilt the lid slightly so the steam can escape. Stir onions every few minutes. Cook for about 15 minutes, or until onions are a golden color.
While onions are cooking, start making your burgers. Place the ground beef in a large bowl. Sprinkle the onion soup mix over the hamburger and then crack the egg over the top. Using clean hands, mix all together thoroughly. Form 4 patties, and then fire up the grill! Cook burgers to your liking. (We cook ours for about 6 to 7 minutes on EACH side.) Add the cheese on top when burgers are almost done. Let the cheese melt slightly, and then place burgers on a platter. Cover to keep warm.
While the burgers are grilling, finish making the carmelized onions. Mix together the water, and beef bullion granules. Pour over the golden onions. Turn the heat to high and let the onions simmer until most of the water evaporates. Remove pan from heat. Stir in the sour cream. Mix until combined.
To build the burgers: Take one cheeseburger and place on bottom bun, then add desired toppings. We like to eat ours with the carmelized onions and lettuce. Some great additional options are barbecue sauce, potato chips and pickles. Place top half of bun over toppings and serve warm! Enjoy!