In a large soup pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion and cook until softened and slightly golden, about 4–5 minutes. Add the garlic and sauté for another minute until fragrant.
Stir in the ground cumin, cinnamon, and nutmeg. Let the spices toast with the onions and garlic for about 30 seconds to bring out their full aroma.
Add your cubed fresh pumpkin (or canned purée if using) into the pot and stir to coat it with the spices. If using fresh pumpkin, cook for an additional 5 minutes to begin softening it.
Pour in the vegetable broth and water. Stir, bring to a boil, then reduce the heat to low and cover. Let the soup simmer for 15–20 minutes, or until the pumpkin is tender.
Remove the pot from the heat. Using an immersion blender, blend the soup directly in the pot until smooth. Alternatively, carefully transfer the soup to a blender and blend in batches. Be cautious with hot liquids.
Return the soup to low heat and stir in the coconut milk (or cream of your choice). Let it gently heat through for 2–3 minutes. Taste and season with salt and pepper as needed.
Ladle the soup into bowls and garnish with your favorite toppings like roasted seeds, a swirl of cream, or chopped herbs. Serve hot with crusty bread.