01 - Heat olive oil in a large pot over medium heat. Add diced onion and cook until softened, approximately 5 minutes.
02 - Incorporate minced garlic and sauté for 1 minute until fragrant.
03 - Stir in tomato paste and cook for another minute to develop flavor.
04 - Add canned tomatoes with their juice, vegetable broth, sugar, salt, black pepper, and optional red pepper flakes. Bring mixture to a simmer.
05 - Reduce heat and simmer uncovered for 20 minutes, stirring occasionally.
06 - Add fresh basil leaves and puree the soup with an immersion blender or in batches using a countertop blender until smooth.
07 - Stir in heavy cream and adjust seasoning as needed. Keep warm over low heat.
08 - Butter one side of each bread slice.
09 - Place 4 slices of bread, buttered side down, on a skillet over medium heat. Top each with 2 slices cheddar and 1 slice mozzarella.
10 - Cover with remaining bread slices, buttered side up. Cook for 2 to 3 minutes per side until bread is golden brown and cheese is melted.
11 - Cut sandwiches in half and serve hot alongside the bisque, garnished with additional fresh basil.