Divide meat into 1/4 lb. patties. Use something heavy or the bottom of a pot to smash the patties between parchment paper to about 1/4" thick.

Turn the griddle on to medium low heat

Slice onions. Put a tablespoon of butter on the griddle with a tablespoon of olive oil. Add all of the onion slices to the griddle and season with salt and pepper.

Sauté the onions until they get soft, then add the Dijon mustard and Worcestershire Sauce to the onion and let cook a few more minutes until combined.

Transfer the onions to a bowl.

Turn the griddle up to medium high and add the burger patties. Season liberally with salt and pepper. Cook until done, then set aside while you assemble the sandwiches.

Lay out all the bread slices. Add a slice of cheese, the burger patty, some caramelized onions and top with another slice of cheese. Butter the top and bottom of each sandwich.

Turn the griddle down to medium low again and add the sandwiches to the griddle. Cook until both sides are browned and serve.