01 - Heat olive oil in a large pot over medium heat. Add diced onion and cook until softened, about 5 minutes.
02 - Stir in minced garlic and sauté for 1 minute until fragrant.
03 - Add tomato paste and cook for an additional minute, stirring frequently.
04 - Add whole peeled tomatoes with their juice, vegetable broth, sugar, salt, black pepper, and red pepper flakes. Bring to a gentle simmer.
05 - Reduce heat and simmer uncovered for 20 minutes, stirring occasionally to meld flavors.
06 - Add fresh basil leaves. Purée the soup using an immersion blender or standard blender until smooth.
07 - Stir in heavy cream and adjust seasoning to taste. Keep bisque warm over low heat until ready to serve.
08 - Butter one side of each bread slice evenly.
09 - Place 4 slices of bread, buttered side down, on a preheated skillet over medium heat. Layer each with 2 slices cheddar and 1 slice mozzarella.
10 - Top with remaining bread slices, buttered side up. Grill each sandwich for 2 to 3 minutes per side until golden brown and cheese has melted.
11 - Cut sandwiches in half and serve immediately alongside the tomato basil bisque, garnished with extra fresh basil.