In 3 qt. saucepan over low heat, melt butter; add sliced onions. Cover and cook, stirring occasionally, until tender, about 20-30 minutes. Add broth, water, bay leaf, pepper and thyme. Increase heat and heat to boiling; reduce heat. Cover and simmer 15 minutes.
Place bread slices on cookie sheet; broil 5" from heat until golden brown, approximately 1 minute. Turn; repeat. Place toasted bread slices in oven-proof bowls or individual casseroles. Add broth and onions; top with Swiss cheese. Sprinkle with Parmesan cheese.
Place bowls on cookie sheet. Broil with cheese about 5" from heat just until cheese is melted and golden brown, 1-2 minutes. Serve with additional French bread or rolls, if desired.