In a large bowl, mix the breadcrumbs and milk. Let soak for 2 minutes. Add the meat, eggs, paprika, and half of the pepper. Season with salt. Mix with hands until well combined, then shape into 8 patties.

In a large skillet over medium-high heat, brown half the patties at a time in the butter for 6 to 8 minutes. Season with salt and pepper. Set aside on a plate.

In the same skillet over medium heat, brown the onions for 5 minutes in the hot fat. Deglaze with the vinegar. Reduce until almost dry. Whisk in the broth, toasted flour, Worcestershire sauce, and remaining pepper. Bring to a boil and simmer until the sauce thickens, stirring occasionally. Remove from heat and stir in the mustard. Return the meat to the skillet and cook for 2 more minutes or until the meat is cooked through. Adjust seasoning.

Serve the hamburger steaks with the sauce and steamed potatoes or mashed potatoes, if desired.