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Over a medium heat, melt butter in a heavy-bottomed saucepan. Add the onions and salt. Sweat the onions for 10 minutes, stirring often.
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Add the mustard and thyme. Stir, turn down the heat to low and cover the pan with a tight-fitting lid. Let the onions cook in their own juices for 35 minutes.
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Add the water, soy sauce, wine, and white pepper. Stir soup, bring to simmer and cook for 10 minutes more.
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Heat the broiler on low heat (if option). Place oven-safe bowls onto a cookie sheet and fill bowls 3/4 full with soup. Cover each soup with a slice of bread and a few slices of Swiss cheese. Put the cookie sheet under the broiler and broil until the cheese is melted. Serve immediately.