In a large skillet, heat the butter and olive oil over medium heat.
Add the sliced onions and cook, stirring occasionally, until they become soft and golden brown, about 15-20 minutes.
Sprinkle the sugar over the onions and continue to cook for another 5 minutes until they are deeply caramelized.
Pour in the beef broth and simmer until the liquid is mostly absorbed, about 10 minutes. Set aside.
Prepare the Burger Patties:
In a mixing bowl, combine the ground beef, salt, black pepper, and Worcestershire sauce. Mix until just combined.
Divide the mixture into 4 equal portions and shape them into patties.
Cook the Burger Patties:
Heat a skillet or grill over medium-high heat.
Cook the burger patties for about 4-5 minutes on each side, or until they reach your desired level of doneness.
Assemble the Burgers:
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