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 uniform oval patties about ¾ inch thick.
02 - Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Sear the patties for 3 to 4 minutes per side until a deep golden-brown crust forms. Remove the patties from the skillet and set them aside on a plate; 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 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 to 2 minutes to form a light roux and cook off the raw flour taste.
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 - Nestle the seared hamburger steaks back into the skillet, spooning some gravy over the top. 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 cooking, toast the split sandwich rolls or hoagie buns until lightly golden. If using cheese, place a slice on each bottom half during the last minute of toasting so it melts.
08 - Place each hamburger steak on a toasted bun and generously spoon the rich onion gravy over the top. Serve immediately while warm.