Preheat oven to 400°F and line a large, rimmed baking sheet with parchment paper or a Silpat® baking mat. Set aside.
Arrange the tomatoes, red peppers, fennel, carrots, shallots, and garlic in a single layer on the prepared baking sheet. Drizzle with olive oil and season with salt and black pepper, to taste. Toss to combine and sprinkle veggies with fresh thyme leaves.
Place baking sheet in preheated oven and roast until vegetables are tender and lightly charred, approximately 20-25 minutes.
Transfer the roasted veggies and any juices from the baking sheet to a large soup pot and add chicken broth. Cook over medium heat, stirring occasionally, until hot and bubbly. Remove from heat.
Using an immersion blender, blend contents of the soup pot until completely smooth. Stir in the coconut milk and fresh basil, and serve immediately. Enjoy!