Preheat an oven to 425°F and position an oven rack in the center.
To prepare cauliflower: On a large rimmed baking sheet, toss the cauliflower and oil until well coated. Lightly season with salt and pepper and transfer to the oven to roast, turning occasionally, until the cauliflower is just tender, about 35 minutes.
To prepare soup: Place a large saucepan on the stove over a medium heat and add the butter. When melted, add the onion and cook until tender, being careful to adjust the heat so that the onions do not brown, about 3 minutes. Add the garlic and shallots, and the coriander and cumin. Cook until fragrant, about 2 minutes.
Add the brandy and stir to deglaze the pan. Simmer until most of the brandy is evaporated. Add the champagne vinegar and simmer until almost dry.
Reserve 4 cauliflower florets to garnish the soup. Add remaining cauliflower, the stock, salt and pepper and simmer gently for 5 minutes to combine the flavors and to cook the vegetables. Once the vegetables are tender, transfer the soup to a blender and purée until smooth; working in batches as necessary and being careful not to fill the blender too full with the hot liquid.
Return the soup to a clean pot and bring to a simmer. Once simmering, add the cream and cook for 3 minutes. Taste and adjust seasoning with salt and pepper as needed. Remove from the heat.
To serve: Ladle soup into bowls, drizzle with truffle oil, top with reserved cauliflower florets and sprinkle with chives. Serve immediately.