Make the pimento cheese, this can be done several days in advance: Combine the cheddar, cream cheese, and mayo in a medium mixing bowl. Add the pimentos, and season with cayenne and kosher salt. Stir until well combined and chill for at least 30 minutes before using.
Divide the meat into 8 portions. Form the beef into loosely packed rounds — like a meatball. Set aside while you prep the grill.
Heat a grill to two-zone cooking. Toast the burger buns over high heat and then set aside. Heat a large griddle or skillet over direct heat. Working in batches of two, add two beef rounds to the skillet at a time – season each with salt, . Let the burgers go until some fat pools at the bottom of the burger. Use a large flat spatula to press down hard on each patty for 2 minutes. The burger should be super thin and have a diameter that is at least two inches wider than the bun (if your pan is too small you may only be able to do one at a time).
When the juices in the middle of the burger start to bubble up, flip the burger. Cook another 2 to 3 minutes then top each patty with a generous spoonful of pimento cheese, stack two patties together and top each with a top bun, then bottom bun — this steams the buns deliciously.
Remove the bottom bun and top with a leaf of butter lettuce then the stacked patties and topped buns.