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In a large heavy pot, heat oil and butter over medium-low heat. Add the onions and garlic and sauté until they are fragrant and soft. Add the thyme.
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Turn the heat down to low and continue to cook for approximately 30 minutes, stirring occasionally, until the onions begin to turn light golden brown.
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Add the wine and cook over medium heat for 3-5 minutes, stirring.
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Add the beef stock and season with salt and pepper to your liking.
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Preheat the broiler setting on the oven.
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Place 6 heat-safe soup dishes on a cookie sheet and ladle in the soup. Place a handful of croutons on top of each dish and immediately top with a handful of the grated cheese and a sprig of thyme. Broil the soup until the cheese starts to bubble and turn brown. Serve immediately (with a salad to round out the meal)!