Divide beef into 8 (3 ounce) portions. Form loosely into balls and refrigerate until ready to use, at least 5 minutes and up to 24 hours.
Heat oil on a griddle or a large cast iron skillet over medium heat. Working in batches, toast Kaiser rolls cut-side down until lightly golden, about 1 minute. Transfer to a serving platter and generously brush cut sides with melted butter.
Increase heat to high. Working in batches, place beef balls onto the hot griddle. Immediately smash each ball with a sturdy metal spatula or burger press into a 1/4-inch thick patty. Season with salt and pepper.
Cook without moving until edges are browned and crisp, 1 to 2 minutes. Flip, top each patty with a slice of cheese, and cook until the second side is browned and cheese is melted, about 1 minute more. Cook to an internal temperature of 160 degrees F (71 degrees C). Transfer to a plate.
To assemble, spread mayonnaise on bottom buns and add desired toppings. Top each with 2 patties and close with top buns. Serve immediately. Recipe developed by Nicole Irwin
