01 - In a large mixing bowl, combine ground beef with salt, pepper, garlic powder, and Dijon mustard. Mix gently until just incorporated, then shape into 4 oval patties approximately 1/2 inch thick.
02 - Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat. Sear the patties for 3 to 4 minutes per side until a deep golden-brown crust forms. Remove from the skillet and set aside — they do not need to be fully cooked through at this stage.
03 - Reduce heat to medium. Add the butter and remaining tablespoon of vegetable oil to the skillet. Add the thinly sliced onions and cook, stirring frequently, for 10 to 12 minutes until softened and deeply caramelized. Stir in the minced garlic and dried thyme, cooking for 1 additional minute until fragrant.
04 - Sprinkle the flour over the caramelized onions, stirring to coat evenly. Cook for 1 to 2 minutes to toast the flour and remove any raw taste.
05 - Gradually pour in the beef broth while stirring constantly to prevent lumps from forming. Add the Worcestershire sauce and ketchup, stirring to combine. Bring the mixture to a simmer and cook for 4 to 5 minutes until slightly thickened.
06 - Return the seared patties along with any accumulated juices to the skillet, nestling them into the onion gravy. Cover with a lid and simmer gently for 10 to 12 minutes until the patties are cooked through and the gravy has reached a rich, thick consistency.
07 - Split each sandwich roll and lightly toast the cut sides in a separate pan or under a broiler until golden.
08 - Place a hamburger steak in each toasted roll and ladle generously with the onion gravy. Serve immediately with additional gravy on the side if desired.