01 - Combine ground beef with kosher salt, black pepper, and smoked paprika in a large mixing bowl. Shape into 4 oval-shaped patties, pressing a slight depression in the center to prevent puffing.
02 - Heat 1 tablespoon 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 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 to 10 minutes until deeply caramelized and rich golden brown.
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 cook out the raw flour taste and form a 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 gentle simmer.
06 - Nestle the seared hamburger steaks back into the skillet, spooning gravy over the top. Cover, reduce heat to medium-low, and simmer for 10 to 12 minutes until the patties are cooked through and the gravy has thickened.
07 - Toast the split sandwich rolls or hoagie buns under a broiler or in a toaster oven until lightly golden. Optionally place a slice of cheese on each bottom half during the last minute to melt.
08 - Place each hamburger steak on a toasted bun and generously spoon the onion gravy over the top. Serve immediately while warm.