Start by preparing your ingredients: peel and cube the pumpkin if using fresh pumpkin, dice the onion, and mince the garlic. Place everything nearby for easy access.
Add a splash of oil to a skillet over medium heat, then sauté the diced onion until it becomes translucent and fragrant, about 3-4 minutes. Toss in the minced garlic and cook for another minute until it’s golden and fragrant.
Transfer the sautéed onion and garlic to the slow cooker, then add the cubed pumpkin, ground cinnamon, nutmeg, and vegetable broth. Stir everything well to combine.
Cover the slow cooker with its lid and cook on low for 4 hours, until the pumpkin is tender and easily mashed with a fork. The house will fill with warm, spicy aromas during this time.
Once cooked, carefully use an immersion blender directly in the slow cooker to purée the mixture until smooth and velvety. Alternatively, transfer the soup to a blender in batches, then blend until smooth.
Stir in the coconut milk or heavy cream to add richness and enhance the creamy texture. Season with salt and pepper to taste, then give it a final stir.
Ladle the soup into bowls, and optionally garnish with a sprinkle of cinnamon or a swirl of cream for presentation. Serve hot and enjoy the cozy, spicy warmth of this easy fall dish.