Melt the butter and olive oil in a large pot over medium heat. Add the sliced onions, sugar, and salt.

Stir occasionally for about 30-40 minutes until the onions are deep golden brown and caramelized.

Once the onions are caramelized, pour in the beef or vegetable broth.

Add thyme, bay leaf, and season with salt and pepper. Bring to a boil and then reduce the heat to a simmer for 20-30 minutes.

While the soup is simmering, preheat your oven to 400°F (200°C).

Place the bread on a baking sheet and toast in the oven until golden brown, about 5-7 minutes.

Remove the bay leaf from the soup.

Ladle the hot soup into oven-safe bowls, top each with a slice of toasted bread, and a generous portion of cheese.

Place the bowls on a baking sheet and broil in the oven for 2-5 minutes, watching carefully until the cheese is bubbling and slightly browned.

Carefully remove the bowls from the oven and let cool slightly. Serve piping hot and enjoy.