Heat the oven to 350°F and grease a 3-quart baking dish with 1 teaspoon of the oil.
Mix the beef, egg, bread crumbs, Worcestershire, 1/2 teaspoon salt and 1/4 teaspoon pepper and shape the mixture into 6 oval patties.
Heat the remaining oil in a large skillet over medium-high heat and brown the patties for 2 minutes per side, then arrange them in the dish.
Cook the onions in the same skillet for 8 to 10 minutes, until golden and soft.
Sprinkle the flour and mustard over the onions, cook for 1 minute, and gradually stir in the broth, remaining salt and remaining pepper.
Simmer the gravy for 3 minutes, pour it over the patties and cover the dish with foil.
Bake for 30 to 35 minutes, until the gravy bubbles and the centers of the patties reach 160°F, then rest for 5 minutes.