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1
In a large, deep skillet over medium-high heat, melt 3 tablespoons of the butter.
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2
Add the onions and stir until they are fully coated.
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3
Cook for 10 minutes, stirring frequently, until the onions are softened.
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4
Reduce the heat to medium-low and continue to cook until the onions begin to brown.
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5
Reduce the heat to the lowest setting and continue cooking the onions until they are very brown.
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6
The onions are done when they are uniformly brown and very soft and the volume is about one-fifth of the original amount.
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7
This will take approximately 1 hour total, but its worth it.
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8
Increase the heat to medium-high and add the remaining tablespoon butter to the onions.
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9
Once the butter has melted, stir in the flour and then cook for 2 minutes.
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10
Slowly add 2 cups of the stock and simmer until thickened, approximately 5 minutes (see Note).
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11
Add the remaining 4 cups stock and the wine, vinegar, salt, pepper, and thyme.
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12
Bring to a simmer, lower the heat, and cook for 5 minutes.
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13
Taste for seasoning and add additional salt and pepper as needed.
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14
Garnish the soup by shredding the cheese directly into the soup and topping with a few croutons.
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15
The soup will keep for up to 5 days in the refrigerator; add the cheese and croutons just before serving.
