Melt butter in large non-stick saucepan; add, cook and stir mushrooms and onions over medium heat until tender and any liquid has evaporated.
Blend in flour; gradually stir in broth, water and Worcestershire sauce. Cook and stir over medium heat until mixture boils. Reduce heat; cover and simmer 10 minutes.
Ladle soup into 4 oven-proof soup bowls. Place 3 slices toasted bread in each bowl; top with cheese. Broil until cheese is melted.