Preheat the oven to 350 degrees F (175 degrees C).
Mix together ground beef, bread crumbs, beaten eggs, onion soup mix, salt, and pepper in a large bowl until well combined. Pour in about 1/2 of the beef broth; continue mixing until mixture is thoroughly moistened. Divide into six equal portions and shape into patties.
Heat a Dutch oven over medium heat. Cook patties in the hot pot until browned, 3 to 5 minutes per side. Discard excess grease, leaving patties in the pot.
Stir together condensed soup, remaining beef broth, and dry mustard in a medium bowl until smooth; pour over browned patties in the pot.
Bake in the preheated oven until patties are no longer pink in the center, about 45 minutes. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C).