Prepare the pumpkin: If using a fresh pumpkin, cut it in half, scoop out the seeds, and peel the skin. Then, chop the flesh into chunks. If using canned pumpkin puree, skip this step.
Sauté the vegetables: In a large soup pot, heat the olive oil over medium heat. Add the chopped onion, garlic, carrots, and celery. Sauté for about 5 minutes or until the vegetables are softened.
Add the pumpkin: add pumpkin puree to the pot.
Season and simmer: Sprinkle in the cinnamon, nutmeg, salt, and pepper. Stir to combine. Pour in the vegetable or chicken broth. Bring the mixture to a boil, then reduce the heat to a simmer. Let it simmer for about 20-25 minutes or until the vegetables are tender.
Blend the soup: If you have an immersion blender, use it to puree the soup directly in the pot until smooth. Alternatively, let the soup cool slightly, then transfer it to a regular blender in batches and blend until smooth. Be cautious when blending hot liquids.
Add cream: Return the blended soup to the pot, and stir in the heavy cream. Heat the soup over low heat, but do not let it boil.
Taste and adjust: Taste the soup and adjust the seasoning, adding more salt and pepper if needed.
Serve: Ladle the hot pumpkin soup into bowls. Garnish with fresh parsley or chives, if desired. Serve with crusty bread for a delightful fall meal.