Combine the broth ingredients with 2 quarts of cold water and bring to a boil. Reduce the heat to low and simmer 20 to 30 minutes. Meanwhile, slice the mushrooms into 1/4-inch strips.
Strain the broth. Add the onion to the broth and cook over low heat 3 to 5 minutes. Add the mushrooms and cook until they are tender, about 35 minutes.
Season to taste with salt and pepper. Ladle into shallow soup bowls and garnish with the thyme.