Bring the broth to a simmer in a saucepan over medium heat and place the roast beef in the broth. Season with salt to taste. Let simmer for about 10-15 minutes.
Place a slice of cheese on each slice of bread, portion the beef onto the bread and close up the sandwich. Reserve the broth and season with salt if needed.
Heat the oil as needed in a non-stick pan over medium-low heat.
Place the sandwich in the pan and cook until golden brown on both sides and the cheese is melted. Then cut in half (you can also use a panini grill or George-Foreman grill to cook the sandwich).
Serve the sandwiches with warm beef broth for dipping and with chips and pickles.