Step 1

Make patties: Combine onion, breadcrumbs, egg, ketchup, mustard, and Worcestershire in a bowl. Gently mix in beef with your hands, being careful not to overmix. Shape into 4 patties. Season with salt and pepper.

Step 2

Heat oil in a large skillet over medium-high heat. Add patties and cook, turning once, until brown and cooked through, 8 to 12 minutes. Transfer to a plate and cover with foil to keep warm; reserve skillet.

Step 3

Make gravy: Reduce heat to medium-low. Add butter, onion, and mushrooms to reserved skillet. Cook, stirring occasionally, until soft, 5 to 6 minutes. Add flour and cook, stirring, until browned, 2 to 3 minutes. Gradually whisk in stock and milk. Simmer until thickened, 8 to 10 minutes. Season with salt and pepper