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 patties about ¾ inch thick.
02 - Heat 1 tbsp olive oil in a large skillet over medium-high heat. Sear the patties for 3–4 minutes per side until a deep brown crust forms. Remove and set aside on a plate.
03 - Reduce heat to medium. Add the remaining olive oil and butter to the skillet. Add the sliced onions and cook, stirring frequently, for 8–10 minutes until deeply golden and caramelized.
04 - Stir in the minced garlic and cook for 1 minute until fragrant. Sprinkle the flour over the onions and stir continuously for 1–2 minutes to form a light roux.
05 - Gradually pour in the beef broth while stirring to prevent lumps. Add the Worcestershire sauce and Dijon mustard. Bring the mixture to a simmer.
06 - Return the seared patties to the skillet, nestling them into the gravy. Cover and simmer for 10–12 minutes until the patties are cooked through and the gravy has thickened.
07 - While the steaks finish cooking, toast the split sandwich rolls until lightly golden. 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 the onion gravy over the top. Serve immediately while warm.