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Heat a large, heavy soup pot over medium heat and add the butter. Sauté the onions, stirring occasionally, until caramelized and soft, 30 to 45 minutes. If a lot of fond builds up on the bottom of the pan, add a splash of water to prevent the onions from burning.
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Stir in the garlic, and cook an additional minute. Sprinkle in the flour, cooking for 1 minute.
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Deglaze with the wine making sure you scrape the bottom of the pan to remove all of the browned bits known as fond. Simmer the wine until almost dry.
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Pour in the stock, and bring to a boil. Reduce the heat to a simmer and cook for 10 to 15 minutes to blend the flavors. Add the thyme, and season with salt and pepper to taste.
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Preheat the broiler to high.
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Ladle the soup into ovenproof soup bowls, and set on a foil-lined sheet tray. Place two slices of bread on top of the soup, and generously cover with the grated cheese.
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Slide the tray onto the bottom rack of the oven. This way the cheese can melt slowly before getting too brown.
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Serve piping hot!
