In 4 litre saucepan, melt butter over medium heat. Add onion and saute until tender. Stir flour, tarragon, salt, and pepper into onion until well mixed. Gradually stir in undiluted broth and water until well combined. Add tomato bits and heat mixture to boiling, stirring constantly. Cover and reduce heat to low. Simmer soup 10 minutes, stirring occasionally.
Meanwhile, peel, seed, and dice tomatoes. Stir undiluted tomato soup, milk, and half-and-half into soup until well mixed. Increase heat to medium-high and heat soup until bubbles appear around side of pan. Do not boil. Stir in diced tomatoes and heat through.
Ladle soup into bowls. If desired, sprinkle soup with chopped herbs and place bowls onto plates garnished with sprigs of herbs.
Note: Dried tomato bits or halves are available in the produce section of most major supermarkets.