01 - In a large mixing bowl, combine ground beef with salt, pepper, garlic powder, and Dijon mustard. Shape the mixture 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 brown crust forms. Remove from the skillet and set aside; they do not need to be fully cooked 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 golden caramelization develops. Stir in the minced garlic and dried thyme, cooking for an additional minute.
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. Bring the mixture to a simmer and cook for 4 to 5 minutes until the gravy begins to thicken slightly.
06 - Return the seared patties and any accumulated juices back to the skillet, nestling them down 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, thickened consistency.
07 - Split the sandwich rolls and lightly toast them. Place one hamburger steak in each roll and ladle the onion gravy generously over the top.
08 - Serve immediately while hot. Offer additional gravy on the side if desired.