Saute onion in butter in a Dutch oven until tender.
Blend in flour, stirring until smooth.
Gradually add chicken broth, beef broth, water, and wine.
Bring to a boil; reduce heat and simmer 15 minutes.
Place 8 ovenproof serving bowls on a baking sheet.
Place 1 bread slice in each bowl; ladle soup over bread.
Top with 1 cheese slice; sprinkle with Parmesan cheese.
Broil 6 inches from heat until cheese melts.