In a heavy soup pot, melt the butter with the EVOO, 2 turns of the pan, over medium-high heat. Stir in the onions, bay leaf and thyme; season with salt and pepper. Cook until the onions are softened and browned, 25 minutes.
Meanwhile, in a large saucepan, bring the chicken broth, mushrooms and 2 cups water to a boil. Lower the heat and simmer for 15 minutes. Using a slotted spoon, remove the mushrooms and slice.
Preheat the broiler. Pour the sherry into the onions and cook over medium heat, scraping up any browned bits. Stir in the mushrooms and hot broth.
Toast the bread under the broiler, rub with the garlic and top with the cheese. Broil until melted. Ladle the soup into bowls and serve with the toasts.