Rehydrate the dried tomatoes by soaking them in warm water for 1 hour. Meanwhile, sweat the onion in the olive oil in a 2-quart saucepan over medium heat, uncovered, for 7 to 10 minutes, stirring occasionally. Do not let the onion color.
Add the stock, rehydrated tomatoes, roasted peppers, fresh tomatoes, salt and pepper and let it all simmer together for 10 minutes. Pour the soup into a blender and process at a high speed for 4 minutes, until very smooth. Then pass it through a strainer to remove the vegetable skins. Adjust the seasoning and serve with fresh basil leaves as a garnish.