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In a large pot, heat the olive oil over medium high heat. Add the onion, carrot, celery, and pepper. Cook until vegetables are tender, about 5 minutes. Add the garlic and bay leaf and cook for one more minute.
Add the chopped sweet potatoes and vegetable broth. Season with smoked paprika, coriander, thyme, salt, and pepper. Partially cover the pot with a lid and simmer for 20 to 30 minutes or until the sweet potatoes are soft when pierced with a fork.
Use an immersion blender to puree the soup in the pot until smooth. You can also carefully transfer the soup to a blender and puree. You will need to do it in two batches, so the blender isn’t too full and make sure you let the soup cool for a few minutes so it isn't too hot.
Stir in the coconut milk. Taste and season with additional salt and pepper, if necessary. Ladle into bowls and serve warm. You can garnish the soup with a drizzle of coconut milk, a dash of smoked paprika, and chopped fresh parsley, If desired.