Heat griddle flat top or large cast-iron skillet over medium heat until hot. Meanwhile, divide beef evenly into four portions. Lightly shape into loose balls. Season with salt and pepper.
Evenly place balls on griddle; cook 1 to 2 minutes or until bottoms are browned and crispy. Turn balls smashing into thin patties with a spatula or burger press. Cook 1 to 2 minutes or until instant-read thermometer inserted horizontally into center registers 71°c. Remove from heat; top each patty with 2 slices of cheese. Keep warm.
Assemble melts by placing half of bread on flat surface; top with patties, basil and remaining bread slices.
