Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and garlic, and sauté for about 2-3 minutes until they become translucent.
Add the chopped carrots and potatoes to the pot. Sauté for another 5 minutes, stirring occasionally.
Stir in the ground cumin and paprika. Cook for an additional minute to allow the spices to bloom and release their flavors.
Add the chopped pumpkin to the pot, and season with salt and black pepper. Stir everything together for a couple of minutes.
Pour in the vegetable broth. Bring the mixture to a boil, then reduce the heat to a simmer. Cover the pot and let it simmer for about 20-25 minutes or until the vegetables are soft and tender.
Once the vegetables are cooked, remove the pot from the heat. Use an immersion blender to puree the soup until smooth and creamy. If you don't have an immersion blender, you can carefully transfer the hot soup to a blender in batches and blend until smooth.
Return the pureed soup to the pot (if necessary) and place it back on low heat. Stir in the heavy cream or coconut milk, and let it simmer for an additional 5 minutes, allowing the flavors to meld together. Adjust the seasoning with more salt and pepper if needed.
Once the soup is heated through, remove it from the heat.
Ladle the crema de calabaza into bowls, and garnish with fresh parsley or chives, if desired.
Serve the Spanish pumpkin soup hot with some crusty bread on the side.