Heat the oil in a large pot over medium heat. Add the onion and cook, stirring often, for 5 to 7 minutes until soft and translucent. Add the garlic and cook for 1 minute until fragrant.

Add the sweet potatoes, vegetable broth, thyme sprigs, salt, and pepper. Bring to a boil, then reduce the heat to low, cover, and simmer for 20 to 25 minutes until the sweet potatoes are very tender.

Remove the thyme sprigs. Use an immersion blender to purée the soup until completely smooth. If using a countertop blender, work in batches, blending for 1 to 2 minutes.

Stir in the coconut milk and maple syrup. Taste and adjust the salt, then add the cayenne if using. Warm over low heat for 2 to 3 minutes; do not boil.

Ladle into bowls and garnish with a swirl of coconut milk, black pepper, and fresh thyme leaves. Serve hot.