01 - In a large mixing bowl, combine ground beef with salt, pepper, garlic powder, and Dijon mustard. 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 brown crust forms. Remove from the skillet and set aside; they will finish cooking in the gravy.
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 brown. Stir in the minced garlic and dried thyme; cook 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 remove the raw flour 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 begins to thicken slightly.
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 the sandwich rolls and lightly toast them. Place one hamburger steak in each roll and ladle a generous amount of onion gravy over the top.
08 - Serve the sandwiches immediately while hot. Offer extra gravy on the side for dipping.