01 - In a large mixing bowl, combine the ground beef with kosher salt, black pepper, and smoked paprika until evenly seasoned. Shape the mixture into 4 uniform oval-shaped patties, about ¾ inch thick.
02 - Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Place the patties in the skillet and sear for 3 to 4 minutes per side until a deep golden-brown crust forms. Remove the patties and set aside on a plate; they will finish cooking in the gravy.
03 - Reduce the heat to medium. Add the remaining 1 tablespoon of olive oil and the butter to the same skillet. Add the thinly sliced onions and cook, stirring frequently, for 8 to 10 minutes until they are deeply golden brown and fully caramelized.
04 - Add the minced garlic to the caramelized onions and stir for 1 minute until fragrant. Sprinkle the flour over the onion mixture and stir continuously for 1 to 2 minutes to cook out the raw flour taste and form a smooth roux.
05 - Gradually pour in the beef broth while whisking constantly to prevent lumps. Stir in the Worcestershire sauce and Dijon mustard. Bring the mixture to a gentle simmer, scraping up any browned bits from the bottom of the skillet.
06 - Nestle the seared hamburger steaks back into the skillet, spooning some gravy over the top. Cover the skillet with a lid and simmer for 10 to 12 minutes until the patties are cooked through to an internal temperature of 160°F and the gravy has thickened to a rich consistency.
07 - While the steaks finish braising, toast the sandwich rolls or hoagie buns cut-side down in a separate skillet or under the broiler until lightly golden. If using cheese, place a slice on each bottom half during the last minute of toasting to melt.
08 - Place each hamburger steak on a toasted bun and generously spoon the onion gravy over the top. Serve immediately while warm.