Combine beef, breadcrumbs, milk, 1 tbsp Worcestershire, garlic powder, onion powder, and half the salt and pepper.
Form six oval patties, about 3/4-inch thick. Chill 10 minutes if soft.
Heat oil in a large skillet over medium-high. Sear patties 2–3 minutes per side until browned. Transfer to a plate.
Lower heat to medium. Melt butter in the same pan. Add onions and remaining salt. Cook, stirring, until golden, 8–10 minutes.
Sprinkle flour over onions. Cook 1–2 minutes, stirring, until it smells toasty.
Whisk in broth gradually. Stir in ketchup, Dijon, remaining Worcestershire, thyme, and remaining pepper. Simmer until slightly thickened, 3–5 minutes.
Nestle patties into the gravy. Cover and simmer until cooked through, 8–10 minutes.
Rest 5 minutes. Garnish with parsley and spoon gravy over the steaks to serve.