Melt butter in a large, heavy saucepan. Add the meat and vegetables and sauté until lightly browned. Sprinkle on the flour; cook briefly over medium heat until the flour has browned. Gradually pour in the beef broth, stirring constantly until the mixture comes to a boil. Add the thyme, bay leaf, salt and pepper. Lower heat; cover and simmer for 2 hours.
Purée soup in an electric blender or use an emersion blender. Reheat; add the Madeira . Check the seasonings. Yield: 4 servings.