Preheat a skillet over medium heat and gently form the ground beef into four evenly-sized patties, seasoning them with salt and pepper.
Lightly coat each patty with flour, pressing gently so they adhere, which helps develop a crispy exterior.
Add olive oil to the hot skillet and sear the patties for about 3-4 minutes per side until golden brown and crusty.
Remove the browned patties from the skillet and set aside on a plate, leaving drippings for the gravy.
Add sliced onions to the skillet with a splash of oil and cook over medium heat, stirring occasionally, until they soften and turn golden brown, about 8-10 minutes. The onions will become sweet and fragrant.
Sprinkle the remaining flour and paprika over the onions, stirring constantly to create a thick, flavorful roux that absorbs the aromatic bits from the pan.
Gradually pour in the beef broth and Worcestershire sauce, stirring constantly to prevent lumps and enable the sauce to thicken into a rich gravy.
Return the seared beef patties to the skillet, spooning some gravy over each piece, and simmer everything together for about 8-10 minutes until the patties are cooked through and the gravy is glossy and flavorful.
Taste the gravy and adjust seasoning with salt, pepper, or extra Worcestershire as desired for a balanced, savory flavor.
Serve the Salisbury steaks hot, topped with the caramelized onions and a generous ladle of the smoky paprika gravy, accompanied by your favorite sides.