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1
Using a mandoline or sharp knife, thinly slice the onions lengthwise. Set aside.
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2
In a large, heavy pot over medium-low heat, melt the butter with the oil. Add the onions, cover and cook, stirring occasionally, adding the sugar and seasoning with salt and pepper, until the onions are meltingly soft, golden and lightly caramelized, 25 to 30 minutes.
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3
Add the wine, increase the heat to high and cook until the liquid is reduced by about half, 8 to 10 minutes. Add the stock and bay leaf, reduce the heat to medium-low and let the soup simmer, uncovered, until it is dark and fully flavored, about 45 minutes. If the liquid is evaporating too quickly and the soup seems to taste too strong, add a little water, then cover the pot and continue cooking.
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4
Just before serving, preheat an oven to 400u00b0F. Arrange the bread slices on a baking sheet and toast, turning once, until golden on both sides, 3 to 5 minutes per side. Remove from the oven and set aside.
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5
Remove the bay leaf from the soup and discard. Arrange 6 ovenproof soup bowls on a baking sheet and ladle the hot soup into the bowls. Place a piece of toast on top of each bowl and sprinkle evenly with the cheese. Bake until the cheese melts and the toasts are lightly browned around the edges, 10 to 15 minutes. Serve immediately.
