How to Make It
Heat a large nonstick griddle or cast-iron skillet over moderately high heat. Toast the hamburger buns cut side down on the griddle until golden brown, 1 to 2 minutes. Transfer to a platter.
Form the beef into four 1/4 inch-thick burgers and season with salt. Increase the heat to high and cook the patties until they are browned on the bottom, about 2 minutes. Flip, top with cheese and cook until the bottom is browned and the cheese is melted, about 2 minutes. Transfer the patties to the bottom buns and top with butter lettuce, tomato and red onion. Spread mayonnaise and ketchup on the cut side of the top buns, if using, and serve.
For a double burger, double the amount of beef and cheese to make 8 patties.