Bring the broth to a simmer in a saucepan over medium heat and place the roast beef in the broth. Let simmer for about 10 to 15 minutes. Remove the beef and lay the meat on the pita and top with cheese.
Place under the broiler to melt the cheese. Taste the broth and season with salt to taste. Serve the sandwiches with small bowls of the warm beef broth for dipping as well as chips and pickles.