Combine the butternut squash, red bell pepper, yellow onion, garlic, water, salt, and sugar in a large soup pot. Bring to a boil, then cover and simmer for 35 minutes.
Using a hand-held immersion blender, purée the soup until silky smooth. Alternatively, cool the soup slightly, then purée in a blender in batches, making sure to leave the hole in the lid open to allow the steam to escape.
Stir in the heavy cream and bring to a simmer. Mix in the thyme (or curry powder), then taste and adjust seasoning.
Ladle the soup into bowls, drizzle with more cream if desired, and serve.