In a mixing bowl, combine the ground beef, egg, mustard, Worcestershire sauce, breadcrumbs, and one packet of onion soup mix. Mix until well combined.
Form the mixture into 5 patties and press them flat so they cook evenly.
Heat olive oil in a skillet over medium heat.
Add the patties and cook for 3 to 4 minutes per side until browned. Remove from the pan and set aside.
Reduce the heat to medium low and add the butter to the same pan.
Once melted, stir in the flour and cook for 3 to 5 minutes, stirring constantly, until it forms a golden roux.
Slowly pour in the beef broth and add ½ can of water, whisking to keep the gravy smooth.
Add a splash of Worcestershire sauce and the second packet of onion soup mix. Stir to combine.
Return the patties to the pan and spoon the gravy over the top.
Let the patties simmer in the gravy until fully cooked through and the sauce has thickened.