Chop the medium onion and mince the garlic cloves if not pre-prepared.
In a large pot, heat the olive oil over medium heat.
Add the chopped onion to the pot and cook until translucent, about 5 minutes. Add the minced garlic and cook for another minute, stirring continuously to prevent burning.
Pour in the vegetable broth and add the pumpkin puree. Stir well to combine.
Add ground cinnamon, ground nutmeg, and ground ginger. Season with salt and pepper to taste. Stir to mix the spices evenly.
Bring the mixture to a boil, then reduce the heat and let it simmer for about 20 minutes, allowing the flavors to meld together.
Using a blender or an immersion blender, puree the soup until it's smooth and creamy. Be careful with hot liquids if using a traditional blender.
Stir in the coconut milk or heavy cream. Let the soup heat through for another 5 minutes but do not let it boil.
Taste and adjust the seasoning if necessary.
Ladle the soup into bowls. Garnish with toasted pumpkin seeds and fresh parsley if desired.