Heat olive oil in a large soup pot over low heat. Add diced onion, celery, and carrots, and sauté for 4 to 5 minutes.
Add garlic, dried thyme, dried parsley, diced sweet potatoes, broccoli, zucchini, and corn. Stir well and cook for 4 to 5 minutes.
Add the vegetable broth and bring to a boil. Reduce the heat and stir in the coconut milk. Simmer for 18-20 minutes, or until the vegetables and sweet potatoes are tender.
Ladle one-third of the soup into a blender. Blend until smooth, then return it to the pot and stir thoroughly. Serve in bowls, garnish with fresh parsley, and enjoy.