Heat the olive oil or coconut oil in a large soup pot over medium heat.
Add the chopped onion, garlic, carrot, and celery. Sauté for about 5 minutes until the vegetables start to soften.
Stir in the diced pumpkin and chopped apple, and cook for another 5 minutes.
Add the ground cinnamon, nutmeg, and ground ginger to the pot. Stir to coat the vegetables and spices evenly.
Pour in the vegetable broth, ensuring that the vegetables are mostly submerged. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for about 20-25 minutes or until the pumpkin and other vegetables are tender and easily pierced with a fork.
Remove the pot from the heat and allow it to cool slightly.
Use an immersion blender to carefully puree the soup until it's smooth and creamy. If you don't have an immersion blender, you can transfer the soup in batches to a regular blender, but be sure to allow it to cool a bit before blending, and blend in batches to avoid splattering hot soup.
Return the pureed soup to the pot and reheat it over low heat. If the soup is too thick, you can add more vegetable broth until you reach your desired consistency.
Season the soup with salt and black pepper to taste. Adjust the spices if necessary, adding more cinnamon, nutmeg, or ginger if you like.
Serve the dairy-free pumpkin soup hot, garnished with roasted pumpkin seeds, fresh herbs, or a drizzle of coconut cream, if desired.
Enjoy your healthy and creamy dairy-free pumpkin soup!