01 - In a large bowl, combine ground beef with kosher salt, black pepper, and smoked paprika. Mix gently and form into 4 oval-shaped patties.
02 - Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add patties and cook for 3 to 4 minutes per side until deeply browned. Remove and set aside — they will finish cooking in the gravy.
03 - Reduce heat to medium. Add the remaining olive oil and butter to the skillet. Add sliced onions and cook, stirring frequently, for 8 to 10 minutes until deeply golden and caramelized.
04 - Stir in minced garlic and cook for 1 minute until fragrant. Sprinkle flour over the onions and stir continuously for 1 to 2 minutes to form a light roux.
05 - Gradually pour in beef broth while stirring constantly to prevent lumps. Add Worcestershire sauce and Dijon mustard. Bring the mixture to a gentle simmer.
06 - Return the hamburger steaks to the skillet, nestling them into the gravy. Cover, reduce heat, and simmer for 10 to 12 minutes until patties are cooked through and the gravy has thickened.
07 - While the steaks finish, toast the sandwich rolls or hoagie buns cut-side down. Optionally place a slice of provolone or Swiss cheese on each bottom half during the last minute of toasting to melt.
08 - Place each hamburger steak on a toasted bun and generously spoon onion gravy over the top. Serve immediately while warm.