Start the soup: In a large pot, combine diced tomatoes, broth, tomato paste, sugar, and basil. Bring to a simmer over medium heat and cook for 10 minutes.
Use an immersion blender to puree the soup until smooth (or carefully transfer to a blender in batches). Stir in cream and season with salt and pepper. Keep warm on low heat.
Butter one side of each bread slice. Place 4 slices butter-side down and top each with 2 cheese slices, then place remaining bread slices on top, butter-side up.
Heat a large skillet or griddle over medium heat. Cook sandwiches for 3-4 minutes per side until golden brown and cheese is melted.
Cut sandwiches in half diagonally and serve immediately with hot tomato soup for dipping. Heaven in a bowl!