Melt butter and olive oil over medium heat in a large Dutch oven or heavy-bottom pan. Once heated, add the sliced onion, minced garlic, brown sugar, and salt to the pan.

Sauté until the onions are soft and caramelized, about 30-35 minutes. Keep an eye on the onions and stir frequently. Add a tablespoon of water if necessary to prevent sticking.

When the onions are caramelized, sticky, and golden brown, sprinkle the gluten-free flour and stir well until fully incorporated.

Once the flour is mixed well with the onions, pour the dry white wine and Worcestershire sauce into the pan and stir again.

Add the beef broth. Simmer for 10-15 minutes until the broth thickens. Season with more salt and pepper if necessary.

Take a ladle of the soup and pour it into 4 oven-safe bowls. Broil in the oven for 2-3 minutes until the cheese is beautifully brown and fully melted. Serve immediately while hot and enjoy.