Mix the meat gently: In a bowl, combine ground beef, breadcrumbs, egg, grated onion, garlic, Worcestershire, Dijon, salt, pepper, and paprika.
Use your hands or a fork to mix just until combined. Don’t overwork—that can make the patties tough.
Form patties: Shape into 4 oval patties about 3/4 inch thick. Press a shallow dimple in the center of each to help them cook evenly and stay flat.
Sear the patties: Heat oil in a large skillet over medium-high. Add the patties and cook 3–4 minutes per side until well browned.
They don’t need to be cooked through yet. Transfer to a plate; tent with foil.
Cook the onions: Reduce heat to medium. Add butter to the same skillet.
Stir in sliced onions with a pinch of salt. Cook 8–10 minutes, stirring often, until soft and golden. If the pan looks dry, add a splash of broth to loosen browned bits.
Toast the flour: Sprinkle flour over the onions.
Stir and cook 1–2 minutes to eliminate raw flour taste. It will look pasty—that’s okay.
Build the gravy: Slowly whisk in beef broth, scraping the pan. Add Worcestershire, soy (if using), and thyme.
Bring to a gentle simmer.
Return patties to the pan: Nestle the seared hamburger steaks into the gravy. Simmer 6–8 minutes, flipping once, until patties are cooked through (internal temp about 160°F/71°C) and the gravy thickens to a silky consistency.
Taste and finish: Adjust salt and pepper. If the gravy is too thick, whisk in a splash of broth.
If too thin, simmer another minute. Garnish with parsley.
Serve: Spoon onions and gravy over the patties. Pair with mashed potatoes, noodles, or rice to soak up every drop.