While onions are cooking, start making the 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.