In a bowl, combine ground beef, breadcrumbs, finely chopped onion, egg, and salt and pepper. Mix gently to avoid dense patties.

Divide the mixture into 4 portions and shape into patties about 3/4-inch thick.

Slice onions for the gravy while the patties rest.

Heat oil in a large skillet over medium-high heat. Add patties and sear for 4–5 minutes per side until browned and cooked to at least 160°F internally.

Transfer patties to a plate and tent with foil to rest.

In the same skillet, reduce heat to medium and add sliced onions with a pinch of salt. Cook until soft and golden, about 8–10 minutes.

Sprinkle flour over the onions and cook for 1 minute.

Gradually whisk in beef broth and Worcestershire sauce, scraping browned bits from the pan. Simmer until gravy thickens, about 3–5 minutes.

Return patties to skillet, spoon gravy over them, and simmer for another 2–3 minutes to warm through.