1. Make the bisque: Preheat the oven to 375°. In a medium saucepan set over medium heat, warm the butter until it has melted and begins to brown, about 5 to 7 minutes. Remove from the heat and set aside.

2. Place the squash pieces on a sheet pan and drizzle with 2 tablespoons of the olive oil. Season with salt and white pepper. Roast in the oven until the squash flesh is fork tender, about 60 to 80 minutes. Remove the squash from the oven and set aside to cool slightly. Scoop out the flesh and discard the skin.

3. Pass the flesh through a food mill (or blend in a blender). Set aside.

4. In a large stockpot set over medium heat, combine the remaining 2 tablespoons of olive oil, onion, garlic and thyme sprigs and cook until the onions are translucent, about 5 minutes.

5. Add the cognac and cook until the liquid is reduced by half, about 6 to 8 minutes. Add the reserved squash and mix well. Add the milk, the reserved brown butter, cinnamon, nutmeg and cloves and reduce the heat to low. Cook for 30 minutes, stirring every few minutes. Stir in the vegetable stock and bring the bisque to a simmer.

6. Carefully transfer the mixture to a blender and blend until smooth. Add the bisque back to the pot; place over low heat and season with salt and white pepper.

7. Make the crème fraîche: In a medium bowl, mix together the crème fraîche, nutmeg, cinnamon, chives and season with salt and white pepper.

8. Ladle the soup into bowls and garnish with spoonfuls of the nutmeg crème fraîche. Serve immediately.