Heat a large pot over medium heat. Add chopped onion and minced garlic. Sauté for about 5 minutes until softened and fragrant, stirring frequently to prevent burning.
Add the cubed purple sweet potatoes. Stir to coat with the onion and garlic. Sauté for an additional 5 minutes.
Pour in the vegetable broth and bring it to a gentle boil.
Once boiling, add the shredded red cabbage. Stir well and let it simmer over medium heat for about 15 minutes until the sweet potatoes are fork-tender.
Reduce heat, pour in the coconut milk, fresh thyme, salt, and pepper. Stir to combine, allowing to warm through for another 5 minutes.
Taste the soup and adjust seasoning if necessary.
Ladle the warm soup into bowls and sprinkle with black sesame seeds before serving.
