Mix together ground beef, chopped onion, garlic and Worcestershire sauce. Season mixture with ground pepper and form into 4 oval patties.
In a large skillet, heat 1 tablespoon of the olive oil over medium heat until hot. Cook patties approximately 5 minutes per side, or until cooked through to desired doneness. Set aside and keep warm.
Pour excess grease out of skillet. Add butter and remaining 1 tablespoon olive oil to pan over medium heat. Add mushrooms and cook until soft, stirring occasionally, around 3 to 5 minutes.
Reduce heat to low, whisk in flour and cook, stirring, for 3 minutes.
Whisk in broth, increase heat to a low boil and cook until thickened, around 3 to 5 minutes. Taste and add salt and/or ground pepper as needed.
Place beef patties on 4 individual serving plates. Spoon mushroom gravy over patties and serve.