In a large pot, over medium heat, heat olive oil and add chopped onion, and celery. Cook for four minutes or until softened and fragrant, stirring occasionally. Next, add garlic cloves and saute for 30 seconds.
Stir in diced sweet potatoes, dried thyme leaves, and salt. Pour in 4 cups of broth, partially cover and simmer for 20 minutes or until sweet potatoes are easily pierced with a fork.
Using a hand-held immersion blender or regular blender, puree soup until smooth. Pour soup back into pot (if using blender) and add coconut milk. Stir to combine. If you would like your soup to be a thinner consistency, add more broth until desired consistency is reached. Season with salt and pepper, to taste. Distribute soup into bowls and sprinkle with chopped parsley or other suggested toppings, if desired.