In a medium bowl, combine the beef, onion, and Worcestershire sauce. Season generously with salt and pepper.
Shape the beef mixture into 4 patties.
Heat the Blackstone (or other outdoor) griddle to medium-high.
Cook the patties, without flipping, until browned and beginning to crisp on the bottom, 4 to 5 minutes.
Flip and use the side of the spatula to break apart the beef patties into pieces. Continue chopping and stirring until the beef is cooked through, about 4 minutes more.
Place a slice of cheese on top of each mound of cooked beef. Cover and let the cheese melt, about 2 minutes.
Spread the mayonnaise, if using, on each side of the cut rolls. Use your spatula to scoop the meat mixture into each roll and top with tomato slices and lettuce. Serve immediately.
Notes
Toast the bun--Want a toasted bun for your sandwich? Use the other side of the griddle to toast the cut sides of the buns while the meat is cooking.
Cheese--It's ok if the cheese isn't fully melted when you scoop the meat off the Blackstone as it will continue to soften and melt in the bun.
Timing--If it's a very cool or very windy day, it may take longer for your meat to cook.