01 - In a large mixing bowl, combine the ground beef with kosher salt, black pepper, and smoked paprika. Gently mix until evenly seasoned, then shape into 4 oval-formed 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 cook for 3 to 4 minutes per side until a deep brown crust forms. Remove the patties and set aside — they will finish cooking in the gravy.
03 - Reduce the heat to medium. Add the remaining 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 deeply golden brown and caramelized.
04 - Stir in the minced garlic and cook for 1 minute until fragrant. Sprinkle the flour over the onion mixture and stir continuously for 1 to 2 minutes to form a smooth roux.
05 - Gradually pour in the beef broth while stirring constantly to prevent lumps. Add the Worcestershire sauce and Dijon mustard, then bring the mixture to a gentle simmer.
06 - Return the hamburger steaks to the skillet, nestling them into the gravy. Cover with a lid and simmer for 10 to 12 minutes until the patties are cooked through and the gravy has thickened to a rich consistency.
07 - While the steaks finish braising, toast the split sandwich rolls or hoagie buns. Optionally, place a slice of provolone or Swiss cheese on each bottom half during the final 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.