Combine ground beef, egg, salt, and pepper in a mixing bowl and mix. Mix it fast but mix it thoroughly.
Shape the patties as quickly as you can and lay them out on a parchment paper covered metal tray.
Season each patty with some more salt and pepper on both sides and cover the tray with plastic wrap.
Refrigerate for 2-4 hours before cooking. (If you need to, you can refrigerate overnight but make sure to cover the tray with plastic wrap air-tight.)
Use your fingers to make a well in the center of each patty, about half way deep, before taking off the plastic wrap.
Preheat a cooking pan over medium to medium high heat with a little oil. The pan should be hot when adding the burgers.
Add burger patties and cook for 5-8 minutes per side, depending on how well you want them. Do not disturb the burgers while cooking.
(Note that these are 1/2 lb patties, they will take a couple minutes longer than thin burgers to cook.)
Take cooked patties out of the pan and let them rest on the plate for about 5 minutes before servings. Tent them loosely with a sheet of aluminum foil to keep warm.
If adding cheese: place a slice of cheese on top of each patty 30-45 seconds before taking it off the pan. Toast the buns: to make the buns nice and toasty, preheat another pan, brush each bun with a little butter on the inside and place them in the pan buttered side down. Let them toast for a couple of minutes.
Disclaimer: Nutrition information shown is calculated for burger patties only! Any additional topping will have to be calculated on case by case bases.