Heat oil in a large heavy-based pot over medium heat and add the onion. Sauté for 3 minutes, then add the garlic, celery, carrots, potatoes, and all the spices. Sauté for a further minute.
Pour in the vegetable broth, add the bay leaves (if using), and bring the soup to a boil.
Then, reduce the heat and let the soup simmer for about 20 minutes, covered, or until the vegetables are tender.
Transfer half the soup to another pot, remove the bay leaves (if used), and blend one half with an immersion blender until smooth.
Alternatively, blend it in a blender, making sure to work in batches, hold down the lid, and avoid overfilling the blender.
This step helps to create an interesting texture of smooth and chunky, which makes this soup really delicious!
Pour the blended soup back into the large pot, add the dairy-free cream, and stir to combine. Allow it to simmer for a few more minutes, taste it, and adjust the seasonings (salt/pepper and red pepper flakes for heat) to your liking.
Serve in bowls, garnish with fresh parsley, and enjoy!