Mix ground beef, eggs, bread crumbs, dry soup mix, salt, and pepper together in a large bowl; add about 1/2 the can of beef broth and continue mixing until beef mixture is thoroughly moistened. Divide mixture into six portions and shape into patties.
Heat a Dutch oven over medium heat. Brown patties in the hot pot, 3 to 5 minutes per side. Spoon excess grease from the pot.
Stir remaining beef broth with cream of mushroom soup and dry mustard in a bowl until smooth; pour over the browned patties.
Bake in 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).
