In a bowl, mix together the ground beef, breadcrumbs, egg, ketchup, Worcestershire sauce, mustard, salt, and pepper.
Form the mixture into 4 oval patties, about 3/4-inch thick. Using your fingertips, press 8-10 dimples in each patty.
Heat the 2 tablespoons butter in a large skillet over medium-high heat. Add the patties and cook until they form a nice golden crust on each side, about 3 minutes per side. Remove to a plate and set aside.
Add remaining 2 tablespoons butter to the skillet. Add mushrooms and onions and cook, stirring occasionally, until soft and golden brown, 6-8 minutes.
Reduce heat to medium, then whisk in flour. Cook, stirring to prevent burning, for 2 minutes.
Pour in beef stock, whisking continuously, then add the ketchup and Worcestershire sauce.
Bring to a simmer, then cook until gravy thickens to your liking, about 10 minutes. Season to taste with salt and pepper.
Nestle patties in the gravy and continue cooking until patties are no longer pink in the center, about 5 minutes. Serve with gravy spooned over the top.
