1. Melt 2 tablespoons butter in a Dutch oven over medium heat. Add onion; cook 10 minutes, stirring occasionally. Add tarragon, if desired, sugar, and garlic; sauté 2 minutes. Add tomatoes, broth, and tomato paste. Increase heat to medium-high, and bring to a boil; partially cover, reduce heat to medium-low, and simmer 30 minutes.
2. Remove from heat; cool 5 minutes. Place half of soup mixture in blender; process until smooth. Return mixture to pan. Repeat procedure with remaining soup mixture.
3. Add half-and-half and heavy cream, stirring with a whisk over low heat. Set aside; keep warm.
4. While soup simmers, place 3 bread slices on a work surface; arrange 2 cheese slices on each of 3 bread slices. Top with remaining 3 bread slices. Spread softened butter on sides of sandwiches. Heat a large nonstick skillet over medium heat. Add sandwiches to pan; cook 4 minutes or until lightly browned. Turn sandwiches over; cook 2 minutes or until cheese melts. Cut each sandwich in half diagonally.
5. Ladle soup into bowls; serve with sandwiches.