Sauté the garlic slices in half of the olive oil over very gentle heat. Add the peppers and fennel and sauté for five minutes. Add the mushrooms and douse with the soup. Simmer on low heat for eight minutes. The vegetables should not become too soft, they should still have bite.
In the meantime, toast the baguette slices. Brush with pressed garlic to taste.
Add the thyme and parsley to the soup, season strongly with salt and freshly ground pepper and bring to the table on the spot.