Stir in onions, shallots, thyme, salt, pepper and bay leaf.
Cook, stirring often, until the onions are very tender and darkened, 40 to 45 minutes.
Stir in broth; bring to a boil over high heat.
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Reduce heat to low; simmer, stirring occasionally, until slightly reduced, 20 to 30 minutes.
Meanwhile, preheat oven to 400F.
Line a baking sheet with foil.
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Brush 1 side of bread slices evenly with the remaining 1 tablespoon oil.
Arrange the bread, oil-side up, on the prepared baking sheet.
Bake until toasted, about 10 minutes.
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Remove from the oven.
Transfer the toasted bread to a plate.
Do not turn the oven off.
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Remove and discard the bay leaf from the soup.
Place 6 ovenproof soup bowls on a clean baking sheet.
Divide the soup among the bowls; top evenly with the toast and cheese.
Bake at 400F until the cheese is melted, bubbling and brown, about 10 minutes.
- Daily Values (DVs) are the recommended amounts of nutrients to consume each day.
(-) Information is not currently available for this nutrient.
