preheat oven to 450°F. toss together tomatoes, onion, garlic and oil; season with salt and pepper. arrange vegetables in a single layer on a rimmed baking sheet until tomatoes are deep brown in spots and onions are tender. about 45 minutes

transfer vegetables and all juice to a large heavy pot. add broth and bring to a rapid simmer. cook until slightly reduced, about 25 minutes.

using an immersion mixer, or the blender method, puree soup nail smooth. stir in tarragon and season with salt and pepper. thin with extra broth if needed. serve with basil and a drizzle of olive oil.