In a bowl, combine ground beef, breadcrumbs, finely chopped 1/4 cup onion, egg, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Mix gently to avoid overworking.

Divide into four portions and shape into oval or round patties about 3/4-inch thick. Press a shallow thumb dent in the center of each to prevent doming.

Heat a large skillet over medium-high and add 2 tablespoons oil. When shimmering, add patties and brown for 3–4 minutes without moving.

Flip and brown the other side for 3 minutes. Remove patties to a plate.

In the same skillet, lower heat to medium and add 1 cup sliced onions and a pinch of salt. Cook, stirring occasionally, for 6–8 minutes until soft and golden.

Sprinkle 2 tablespoons flour over the onions and stir for 1 minute.

Gradually whisk in 1 cup beef broth while avoiding lumps. Add 1 tablespoon Worcestershire sauce and bring to a simmer.

Nestle the patties back into the gravy, cover, and simmer on low for 8–10 minutes until internal temperature reaches 160°F (71°C).

Let patties rest for 3–5 minutes before serving.