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 the heat to medium. Add the butter and remaining tablespoon of vegetable oil to the skillet. Add the 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 1 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 eliminate the raw taste.
05 - Gradually pour in the beef broth while stirring constantly to prevent lumps. Add the Worcestershire sauce and ketchup. Bring the mixture to a simmer and cook for 4 to 5 minutes until the gravy slightly thickens.
06 - Return the seared patties and any accumulated juices to the skillet, nestling them into the onion gravy. Cover with a lid and simmer for 10 to 12 minutes until the patties are cooked through and the gravy reaches a rich, thickened consistency.
07 - Split the sandwich rolls and lightly toast them. Place one hamburger steak in each roll and generously ladle the onion gravy over the top.
08 - Serve immediately while hot, with extra gravy on the side if desired.