In a large pot, heat a drizzle of olive oil over medium heat. Add the chopped onion and minced garlic, sautéing for about 5 minutes until the onion is translucent and fragrant.

Incorporate the cubed purple sweet potatoes into the pot. Stir gently to coat with the onion and garlic mixture and sauté for an additional 5 minutes.

Pour in the vegetable broth and bring the mixture to a gentle boil. Reduce the heat to maintain a simmer for about 10 minutes.

When the sweet potatoes are nearly fork-tender, stir in the finely shredded red cabbage. Cook for about 15 minutes, stirring occasionally.

Reduce the heat to low and carefully stir in the coconut milk along with fresh thyme, salt, and pepper. Allow the soup to warm through for about 5 minutes.

Taste the soup and adjust seasoning as necessary, adding more salt or pepper to your preference.

Ladle the warm soup into bowls and sprinkle with black sesame seeds before serving.