Preheat oven to 425 degrees F. Rub tomatoes with olive oil, cut in half, and place on oiled baking pan. Bake, turning tomatoes every 10 minutes, until skins blister and blacken, about 30 minutes. Allow to cool, peel and discard skins, reserving pulp and juice. While tomatoes roast; tie parsley and tarragon sprigs together securely with string (a bouquet garni), leaving a length of string attached so that it can be easily retrieved from soup.

Melt butter in a medium saucepan over low heat. Add onion, carrot, and fennel (if using), saute until very soft, 5 to 6 minutes. Add stock and bouquet garni, simmer for 30 minutes. Remove bouquet garni, add tomato pulp and juices. Allow soup to cool and puree using an emersion blender or puree in a regular blender or food processor. Season with salt and pepper, to taste. Stir in buttermilk. Cover tightly with foil or plastic wrap and refrigerate until thoroughly chilled, 1 to 2 hours. Serve sprinkled with fresh dill.

To serve hot: Replace the buttermilk with an equal amount of half-and-half and simmer over low heat, stirring frequently, until heated through.