**Roast the Vegetables:** Preheat your oven to 400°F (200°C). On a large baking sheet, spread out the tomatoes, shallots, and garlic cloves. Drizzle with olive oil and balsamic vinegar. Sprinkle with smoked paprika, salt, and pepper. Toss everything to coat evenly. Add the sprigs of fresh thyme on top.
**Bake:** Roast for 30-40 minutes, stirring halfway through, until the tomatoes are deeply caramelized and the shallots are tender and slightly charred. The garlic should be soft and fragrant.
**Blend the Soup:** Carefully transfer all the roasted vegetables, including the thyme leaves (discard the woody stems), and any juices from the baking sheet into a blender. Pour in the vegetable or chicken broth. Blend until the soup is completely smooth.
**Finish on the Stove:** Pour the blended soup into a saucepan and place over medium heat. Stir in the coconut milk or heavy cream if you are using it. Simmer gently for 5-10 minutes to allow the flavors to meld. Taste and adjust seasoning if needed.
**Serve:** Ladle the hot soup into bowls. Garnish with a few fresh basil leaves, a drizzle of olive oil, or toasted croutons.