Heat 2 tablespoons oil in a 2-quart saucepan over medium-high heat. Add onions and carrots and saute until tender, about 5 minutes. Add garlic and saute until just fragrant. Season with salt and pepper. Add tomato paste and cook until toasted, just 1 more minute.
Add tomatoes, red peppers, and chicken broth and let simmer for 25 minutes, until the vegetables are tender and the flavors have melded together. Taste for seasoning and add more salt, pepper, and the sugar, if needed. Add half-and-half and basil, and puree using a hand held immersion blender until smooth.
Serve in soup bowls with a sprinkle of fresh basil on top.