Place the cauliflower and onion in a pot. Add the water and salt, and bring to a boil over high heat. Reduce the heat to medium-low, cover, and simmer until the cauliflower is very soft, 10 to 15 minutes.
Puree the cauliflower, onion, and cooking water with an immersion blender. Add more water as needed to make a thick, creamy consistency.
Adjust the seasoning to taste. Garnish with freshly ground black pepper, parsley, and heavy cream, if desired (use 1 to 2 tablespoons per serving). Serve hot.
TIP: The key to this soup is to get a thick creamy texture and to add enough salt for it to taste delicious. The original recipe has no fat in it and is perfect to accompany a high-fat mea. If you're having a lower-fat meal, garnish the soup with heavy cream. This soup is great made a day ahead and served chilled or reheated before serving.