Preheat broiler. Coat a baking sheet with cooking spray then set aside.

Core tomatoes. Cut onion in half then peel. Place tomatoes and onions on the baking sheet then drizzle with 1 Tbsp olive oil. Toss tomatoes and onions with oil to ensure all surfaces are covered.

Place on top rack under the broiler for 5 minutes. Turn broiler off then turn oven to 450 degrees. Place baking sheet on lower rack and roast for 10–15 minutes until they char slightly. Flip the tomatoes and onions after 5 minutes.

Place 2 Tbsp oil in a large soup pot or Dutch oven over medium heat. Add carrot and thyme then cook for about 4 minutes, stirring frequently. Add the garlic and cook for 1 minute. Add chicken broth, chicken bouillon or salt and basil. Bring to a boil then reduce heat to medium-low and simmer for 15–20 minutes. Remove thyme sprigs.

Remove tomatoes and onions from oven and transfer to soup. Add tomato paste and simmer for 10 minutes.

Purée soup using an immersion blender or regular blender. If using a regular blender, be sure to work in batches and do not fill the pitcher more than ⅓ full to avoid overflow.

Season with balsamic vinegar, salt, pepper and a pinch of sugar and serve.