In a large bowl, combine ground beef, breadcrumbs, egg, Worcestershire sauce, ketchup, garlic powder, onion powder, salt, and pepper.
Shape the mixture into four oval patties approximately 3/4 inch thick.
Heat vegetable oil in a large skillet over medium-high heat. Sear the patties for 3-4 minutes per side until browned. Remove from skillet and set aside.
In the same skillet, melt butter. Add mushrooms and onions, sautéing until browned and tender, about 5-7 minutes.
Sprinkle flour over the vegetables and stir for 1 minute to cook out the raw flour taste.
Slowly whisk in the beef broth and Dijon mustard. Bring to a simmer until the gravy begins to thicken.
Return the beef patties and any accumulated juices to the skillet. Lower heat to medium-low and simmer for 5-10 minutes until the beef is cooked through and gravy is thick.
Adjust seasoning with salt and pepper to taste and serve immediately.