Slice the onions into thin slices and separate into rings. Place them in a Dutch oven and sauté in butter until tender.
Blend in the flour with the onions, stirring until smooth. Gradually add the chicken broth, beef broth, water, and wine. Bring to a boil, then reduce the heat and simmer for 15 minutes. Add the white pepper.
Place eight soup crocks on a sheet pan. In each bowl, place a slice of bread. Ladle the soup over the bread. Top with a slice of cheese; sprinkle parmesan cheese on top. Broil 6 inches from the heat until the cheese melts.