01 - Heat olive oil in a large pot over medium heat and cook diced onion until softened, about 5 minutes.
02 - Add minced garlic and sauté for 1 minute until fragrant, then stir in tomato paste and cook for an additional minute.
03 - Add whole peeled tomatoes with juice, vegetable broth, sugar, salt, black pepper, and red pepper flakes; bring to a simmer.
04 - Reduce heat and simmer uncovered for 20 minutes, stirring occasionally.
05 - Add fresh basil leaves and puree bisque until smooth using an immersion blender or countertop blender in batches.
06 - Stir in heavy cream, adjust seasoning as needed, and keep warm over low heat.
07 - Butter one side of each bread slice thoroughly.
08 - Place 4 slices of bread, buttered side down, on a heated skillet; top each with 2 cheddar slices and 1 mozzarella slice.
09 - Cover with remaining bread slices, buttered side up; cook 2 to 3 minutes per side until golden and cheese melts.
10 - Cut sandwiches in half and serve hot alongside the bisque, garnished with extra basil.