Place a cast iron skillet or griddle on your grill. Turn the grill to high heat and close the lid. Let it heat up for several minutes, until it is very hot. (You can also make these on the stovetop; set your skillet over medium-high heat.)
Brush the skillet with vegetable oil.
Take 1/4 pound of ground beef straight from the package. Loosely shape it into a ball if you need to (depending on the shape of the ground beef you bought, you may not even need to do any shaping. If it came from the store in a nice tall mound, you might just need to grab a hunk.) Do NOT pack.
Place the ball of meat on the oiled skillet. Work in batches if you need to; I can fit 2 at a time on my skillet. (Need to get myself a griddle!)
Season with a generous amount of salt. Salt is your friend. Add some pepper if you want, but not necessary.
Close the lid of your grill (no need to cover if you're on the stovetop.) Let cook undisturbed for about 2 minutes, until the outer edges are brown.
Flip the burger, season with more salt, and place two slices of American cheese on the burger. Cook until the cheese droops, about 1 more minute. This is for medium rare. Remove from the skillet.
Serve with a soft warm bun, lots of mayonnaise, and whatever over toppings you want. You really can't go wrong. You could even get crazy and stack 2 patties together for a double decker. (2 thin patties is way better than 1 too-thick patty.)