Mix ground beef, breadcrumbs, milk, egg, Worcestershire, Dijon, onion powder, garlic powder, salt, and pepper in a bowl. Gently form into 4 oval patties.
Heat olive oil in a skillet over medium. Brown patties for 4–5 minutes per side until cooked through. Set aside.
Melt butter in the same skillet. Add onions and mushrooms; cook for 6–7 minutes until soft and browned.
Sprinkle flour over vegetables; stir for 1 minute. Slowly whisk in beef broth. Add Worcestershire, salt, and pepper. Simmer 4–5 minutes until thick.
Return patties to skillet. Spoon gravy over them and simmer on low for 5 minutes.
Serve hot over mashed potatoes, rice, or noodles. Top with extra gravy.