1
Preheat the oven to 400°F. Wrap the garlic in tin foil, drizzle with olive oil, and roast until very tender and fragrant, about 20 minutes.
2
Remove the roasted garlic cloves from the head and toss with the walnuts, dill, sugar, walnut oil and vinegar in a small bowl. Adjust the seasoning with salt and pepper.
3
Meanwhile, melt the butter in a large saucepan. Add the onion and garlic and cook on low heat until softened but not colored, about 5 minutes.
4
Stir in the thyme, mushrooms, broth, brandy and cream. Bring to a simmer and cook for 20 minutes, until the mushrooms are tender.
5
Purée the soup with an immersion blender or a regular blender (let it cool first a bit to avoid splashing). Season with salt and pepper.
6
To serve, divide the soup between bowls, garnish with walnut-dill relish and serve with baguette on the side.