Preheat your oven to 400°F (200°C). Cut sweet potatoes into wedges and arrange them on a baking sheet. Drizzle with olive oil and season with salt and pepper, tossing to coat evenly. Roast for 25-30 minutes, or until they're tender and caramelized around the edges.

While the sweet potatoes roast, heat a tablespoon of olive oil in a large pot over medium heat. Add diced onion and sauté for about 5 minutes until softened and translucent. Then, add minced garlic along with dried thyme, rosemary, and basil, cooking for another 1-2 minutes.

Once the sweet potatoes are roasted, add them directly to the pot with sautéed onions and garlic. Pour in vegetable broth, stir to combine, and bring to a gentle boil over medium-high heat. Reduce heat to low and let simmer for about 10-15 minutes.

Use an immersion blender to puree the soup until smooth and creamy. Alternatively, transfer the soup in batches to a traditional blender, blending until desired consistency is reached.

Return the blended soup to the pot if it was transferred. Stir in coconut milk or heavy cream, letting it heat through for about 5 minutes over low heat. Taste and season with additional salt and pepper as needed.

Ladle the warm soup into bowls, garnish with reserved roasted sweet potato wedges, and sprinkle fresh thyme on top. Serve warm with crusty bread or a side salad.