Mix the beef, breadcrumbs, egg, ketchup, Worcestershire, salt and pepper just until combined and shape into 6 oval patties.
Heat the oil in a large skillet over medium-high heat and brown the patties for 3 minutes per side; transfer them to a plate.
Cook the onions in the same skillet for 10 minutes until deep golden and soft.
Sprinkle the flour over the onions, stir for 1 minute, then whisk in the broth and mustard and simmer for 3 minutes.
Return the patties, cover and simmer for 10 to 12 minutes until their centers reach 160°F and the gravy coats a spoon.