In a large bowl, combine the ground beef, breadcrumbs, ketchup, Worcestershire sauce, Dijon mustard, beaten egg, onion powder, garlic powder, salt, and pepper. Mix gently with your hands until just combined, being careful not to overwork the meat. Shape the mixture into 6 oval patties, about 3/4-inch thick.

Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the patties and cook for 3-4 minutes per side until a deep brown crust forms. They will not be cooked through. Remove from the skillet and set aside.

Reduce heat to medium. Add the remaining olive oil, sliced onions, and mushrooms. Cook until softened and browned, about 10-12 minutes total. Stir in the minced garlic and cook for 1 minute. Sprinkle the flour over the vegetables and stir for 1 minute to cook out the raw taste. Gradually whisk in the beef broth and the remaining tablespoon of Worcestershire sauce until smooth.

Bring the gravy to a simmer. Taste and season with salt and pepper. Return the patties and any juices to the skillet. Reduce heat to low, cover, and simmer for 15-20 minutes, until the patties are cooked through and the gravy has thickened. Serve hot.