In a large nonstick skillet, heat oil over medium heat.
Add onions, thyme, and 1 tablespoon of water.
Cover; cook for 5 minutes.
Uncover; reduce heat to medium-low.
Cook until onions are golden, stirring, about 15-20 minutes.
Add garlic; saute for 1 minute.
Add flour; reduce heat to medium.
Cook, stirring, for 2 minutes.
Stir in the broth, remaining water, and nutmeg.
Bring to a boil; skim off foam.
Reduce heat to low; cover and simmer for 30 minutes.
Place 4 heat proof bowls on a baking sheet; ladle soup into bowls.
Top each with a slice of French bread; spinkle with Swiss cheese and Parmesan.
Broil until cheese is bubbly, about 1 minute.