Combine the ground beef, breadcrumbs, egg, milk, minced onion, ketchup, Worcestershire sauce, garlic powder, kosher salt, and black pepper in a large bowl. Mix only until the ingredients are combined.

Divide the mixture into four oval patties about 3/4 inch thick. Press a slight indentation into the center of each patty to help it cook evenly and reduce doming.

Heat a large skillet over medium-high heat with a small amount of oil. Brown the patties for about 3–4 minutes per side, then transfer them to a plate; they do not need to be fully cooked yet.

Reduce the heat to medium and add the butter or oil. Cook the sliced onion and mushrooms for about 5–7 minutes, stirring occasionally, until softened and lightly browned.

Sprinkle the flour over the vegetables and stir for about 1 minute. Gradually whisk in the beef broth, then add the Worcestershire sauce, Dijon mustard if using, and black pepper.

Return the patties and any accumulated juices to the skillet. Cover and simmer gently for 10–15 minutes, turning the patties once, until the beef is cooked through and the gravy has thickened.

Check that the ground beef reaches an internal temperature of 160°F. Taste the gravy and add salt as needed, then spoon the onion-mushroom gravy over the steaks before serving.