Melt the butter in a Dutch oven and add in the sliced onion.
Cook on low heat until the onions are beautifully golden and caramelized, about 30 minutes. Stir occasionally. The longer you cook the onions, the sweeter and more flavor they will have.
Add in the minced garlic, and cook for just a minute.
Add in the wine, bay leaf, thyme, salt, pepper and broth.
Bring it to a boil, reduce the heat and simmer for 20 minutes.
Discard the bay leaf and the thyme stems.
Whisk together the tapioca starch and the water. Add them to the soup. Let it cook for just a couple more minutes.
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Notes
Traditionally, French onion soup is served in a dish with a toasted baguette and Gruyere cheese melted over the top.