Sauté the ground beef in a medium-size skillet over medium heat. Sprinkle with 1 teaspoon salt and the black pepper. Continue cooking while crumbling the beef with your spoon until the beef is well browned. Drain the fat from the beef and set aside.
In a medium-size pot over medium heat, add the chopped onion and vegetable oil and sprinkle with 1 teaspoon salt. Stir and cook the onions until they become translucent.
Sprinkle the flour over the onions and cook for about 1 minute or until the flour becomes fragrant (it should smell like pie dough).
Add about 1/2 cup chicken broth into the pot, and stir until the mixture thickens.
Add another 1/2 cup broth, and stir until this thickens.
Then add the remaining 1 cup broth and stir until the mixture thickens.
Add the potatoes to the soup and cook for about 15 minutes.
Add the ground beef, cheese (reserve some for garnish), dry mustard, and Worcestershire sauce. Stir until well blended, and simmer until the soup is heated through.
While the soup is heating, cut a hamburger bun into 1/2-inch cubes.
Toast the bread cubes in a small skillet with the butter until they have browned. Stir occasionally, so the bread does not burn.
To serve, ladle the soup into bowls and garnish with toasted hamburger buns, dill pickle relish, crumbled bacon, green onions, and the reserved grated cheese.