For the Garlic:

Preheat the oven to 350°F.

With a sharp knife, slice about ½ inch off the top of the head of garlic. Stack two 6-inch squares of aluminum foil. Place the garlic in the center and lift the sides to form a cup. Drizzle with the olive oil and sprinkle with the oregano, salt, and pepper. Enclose by twisting the edges of the foil together to seal.

Place on a baking sheet and roast 20 to 25 minutes, until entirely softened. Open the foil and set aside to cool. When cool enough to handle, squeeze to remove the garlic cloves, discarding the skins.

For the Soup:

Heat the olive oil in a large heavy saucepan over low heat. Add the onion and cook 5 minutes. Add the carrots, leek, celery, thyme, bay leaves, salt, and pepper. Cook, stirring occasionally, about 20 minutes, until the vegetables are very soft and golden. Pour in the stock, increase the heat to high, and bring to a boil. Reduce to a simmer and cook, uncovered, 10 to 20 minutes.

Transfer 1 cup of the stock to a blender. Add the roasted garlic and puree. Pour the garlic mixture back into the soup pot, along with the cream. Adjust the seasonings and continue cooking over medium heat just to heat through. With a slotted spoon, remove the bay leaves and bunch of thyme.

Sprinkle the toasted garlic bread with the grated cheese. Ladle the soup into bowls and top each with a slice of garlic cheese bread and a sprig of thyme. Serve hot.