In a medium saucepan, saute onion and garlic. Add beef broth and bring to a boil. Mix in ketchup.
Sprinkle flour over surface, stirring briskly to avoid lumps (or make a slurry of the flour with a small amount of cold water).
Simmer over medium heat 5 minutes. Add the sliced mushrooms.
Add the sliced beef to the gravy and allow it to simmer several minutes until hot. Remove from gravy and place on slices of white bread or toasted sandwich rolls. Pour gravy over the top, salt and pepper to taste, and serve.