01 - In a mixing bowl, combine the ground beef, breadcrumbs, egg, Worcestershire sauce, garlic powder, onion powder, salt, and black pepper. Mix gently until just combined, being careful not to overwork the meat. Shape the mixture into 4 oval-shaped patties of even thickness.
02 - Heat a large skillet over medium-high heat and add a light coating of oil if needed. Sear the patties for 3 to 4 minutes per side until a deep golden-brown crust forms. Remove the steaks from the skillet and set them aside on a plate. They will finish cooking in the gravy.
03 - Reduce the heat to medium. Melt the butter in the same skillet, then add the thinly sliced onions. Cook, stirring frequently, for 10 to 12 minutes until the onions are deeply golden and caramelized, scraping up any browned bits from the bottom of the pan.
04 - Sprinkle the flour evenly over the caramelized onions and stir constantly for 1 to 2 minutes to cook out the raw flour taste and form a roux.
05 - Slowly pour in the beef broth while stirring continuously to prevent lumps. Add the Worcestershire sauce and dried thyme. Bring the mixture to a gentle simmer, allowing it to begin thickening.
06 - Return the seared hamburger steaks to the skillet, nestling them into the gravy. Spoon the onion mixture over the top of each patty. Cover the skillet and simmer for 10 to 15 minutes until the steaks are cooked through and the gravy has thickened to a rich consistency.
07 - While the steaks finish cooking, brush the split sandwich rolls with melted butter. Toast them in a separate skillet or under a broiler until golden and lightly crisp.
08 - Place a cooked hamburger steak on the bottom half of each toasted bun. Ladle generous spoonfuls of onion gravy over the steak. Add sliced cheese if desired, then cap with the top half of the bun. Serve immediately while hot.