In a large pot, melt the butter over medium heat and add the sliced onions. Cook until deeply caramelized, stirring occasionally, about 15-20 minutes.

Add the chicken broth, thyme, and season with salt and pepper. Bring to a simmer.

Stir in the shredded chicken and let simmer for another 5 minutes.

Preheat the broiler. Ladle the soup into oven-safe bowls, top with a slice of French bread and a generous amount of cheese.

Broil the bowls until the cheese is bubbly and golden. Serve hot.