In a small bowl, mix mayonnaise, ketchup, yellow mustard, and Worcestershire sauce until smooth. Set aside.
Thinly slice the yellow onion and prepare the brioche buns.
Heat a heavy skillet or pan over medium-high heat until very hot.
Divide the ground beef into loose balls. Place each ball onto the hot pan.
Use a spatula to smash each beef ball flat. Season with salt and black pepper.
Add sliced onions on top of each patty and let the burger cook until crispy on the bottom.
Flip the burgers, place a slice of American cheese on each patty, and cook until the cheese melts.
Lightly toast the brioche buns in the pan.
Spread burger sauce on the buns, add the smash patty with onions, and assemble the burgers.
Serve immediately while hot and juicy.