In a 4-quart soup pot over medium heat, combine the olive oil, red, white, yellow, and pearl onions, and the shallots and saute until golden brown and soft.
Add the leeks and chives and cook until the onions turn a deep golden brown, about 5 minutes. Add the wine and cook, stirring, 2 minutes more, or until the mixture begins to bubble.
Add 2 cups of stock every 15 minutes for the next 45 minutes, allowing the liquid to reduce by one-fourth after each addition.
Add the mushrooms and thyme leaves with the last 2 cups of stock. The soup will be a very deep brown. Ladle into deep soup bowls and garnish with thyme sprigs.