01 - In a large mixing bowl, combine ground beef with salt, black pepper, garlic powder, and Dijon mustard until evenly seasoned. Shape 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 patties for 3 to 4 minutes per side until a deep brown crust forms. Remove from the skillet and set aside; the patties do not need to be fully cooked at this stage.
03 - Reduce heat to medium. Add butter and the 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 brown. Stir in minced garlic and dried thyme, cooking for 1 additional minute until fragrant.
04 - Sprinkle flour over the caramelized onions, stirring constantly to coat evenly. Cook for 1 to 2 minutes to toast the flour and eliminate any raw taste.
05 - Gradually pour in beef broth while stirring continuously to prevent lumps from forming. Add 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 beef patties and 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, coating consistency.
07 - Split the sandwich rolls and lightly toast them. Place one hamburger steak in each roll and ladle generously with onion gravy.
08 - Serve immediately while hot. Additional warm gravy may be served on the side for dipping.