Heat the olive oil in your large pot over medium heat. Add the chopped onion and sauté for about 5 minutes, or until softened and translucent. Stir in the minced garlic and ginger, cooking for another 1-2 minutes until fragrant.
Sprinkle the ground cumin and ground coriander over the aromatics. Stir continuously for about 30 seconds to toast the spices, releasing their full flavor.
Pour in the pumpkin puree and vegetable broth. Stir well to combine all ingredients. Bring the mixture to a gentle boil, then reduce the heat and let it simmer for 15 minutes to allow the flavors to meld beautifully.
Using an immersion blender, carefully puree the soup directly in the pot until smooth and creamy. Alternatively, you can transfer the soup in batches to a blender. Return the soup to the pot once blended.
Pour in the coconut milk and stir to incorporate it evenly. Season with salt and pepper to taste. Warm the soup gently for another 5 minutes without boiling to keep the coconut milk from separating.
Ladle the soup into bowls, garnish with fresh cilantro leaves, and enjoy immediately.