Peel and halve the onions. Then slice them.
Heat the butter in a soup pot over medium heat. Add the onions and sprigs of thyme, stir well, set the heat to low and cover. Cook for about 20 minutes.
Remove the lid, turn up the heat a bit and cook the onions until they are caramelized and the liquid is evaporated - about 10 or 15 minutes more.
Stir in the Marsala wine and allow it simmer for a few minutes so the alcohol content evaporates.
Stir in the shredded chicken, beef consommé and chicken stock. Bring the soup to a simmer and allow to cook, uncovered, for 20 minutes.
Taste the soup. Add salt if necessary.
Ladle the soup into bowls or oven-safe ramekins.
Top the soup with toasted sourdough bread cubes. Top the soup with shredded cheese. Serve.
Or, heat the broiler and place the bowls of soup under the broiler for a few minutes to make the cheese browned and bubbly.