In a large pot, heat olive oil over medium heat. Add onion, cover, and cook until soft, stirring occasionally, about 8 minutes. Add 3 cups water, cauliflower, and heavy cream and bring to a boil. Lower heat to medium-low and simmer until cauliflower is soft, about 25 minutes. Stir in crème fraîche.
Working in batches, puree cauliflower mixture in a blender until very smooth. Return soup to pot, add Parmesan and salt, and bring to a gentle simmer.
Ladle soup into bowls and garnish with chives. Drizzle with truffle oil, if using, and serve.