Preheat the oven to 400°F. Line a baking sheet with foil. Put the tomato and pepper halves in a bowl and drizzle with oil. Sprinkle with a pinch of salt. Lay cut side down on the baking sheet and roast for 40 minutes. Remove from the oven and place the peppers in a closed plastic bag for 15 minutes. Remove the peppers from the bag and discard the seeds and skin before chopping. In a soup pot, sauté the garlic, carrot, and onion until translucent. Add the roasted tomatoes and peppers and the broth. Cover and cook on low for 30 minutes.
Add the sugar. Using a hand blender, purée the mixture until smooth. Add salt and pepper.