In a large bowl, combine the ground beef, egg, breadcrumbs, Worcestershire sauce, garlic powder, onion powder, salt, pepper, ketchup, and Dijon mustard. Mix gently with your hands until just combined. Overmixing can make the patties tough, so stop as soon as the ingredients come together.

Shape the mixture into four oval patties. Try to keep them roughly the same thickness so they cook evenly.

Heat a large skillet over medium heat and add a drizzle of oil. Place the patties in the pan and cook for 4 to 5 minutes per side until browned. They do not need to be cooked through at this stage. Browning them adds deep flavor, so give them time to get a nice sear.

Remove the patties and set them aside on a plate. In the same skillet, melt the butter and add the sliced onions. Cook for 5 to 7 minutes until the onions soften and turn golden. This step builds the foundation of the gravy, so keep the heat steady and stir occasionally.

Sprinkle the flour over the onions and stir well. Cook for 1 minute to remove the raw flour taste. The mixture should look like a thick paste.

Slowly whisk in the beef broth, making sure to dissolve any lumps. Add the Worcestershire sauce and ketchup. Bring the gravy to a gentle simmer and let it thicken slightly.

Return the patties to the skillet, nestling them into the gravy. Cover and simmer for 12 to 15 minutes, or until the patties are fully cooked and the gravy has thickened to your liking.

Taste the gravy and adjust the seasoning with salt and pepper. If you prefer a richer flavor, add mushrooms or finish with a splash of cream. Garnish with fresh parsley before serving if desired.