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 1 minute to deepen flavor.
04 - Add whole peeled tomatoes with their juice, vegetable broth, sugar, salt, black pepper, and crushed red pepper flakes. Bring mixture to a simmer.
05 - Reduce heat to low and simmer uncovered for 20 minutes, stirring occasionally to meld flavors.
06 - Incorporate fresh basil leaves. Blend soup until smooth using an immersion blender or by carefully transferring in batches to a blender.
07 - Stir in heavy cream and adjust seasoning as needed. Keep warm over low heat until serving.
08 - Butter one side of each bread slice evenly for grilling.
09 - Place four bread slices, buttered side down, onto a heated skillet over medium heat. Top each with two slices of cheddar and one slice of mozzarella cheese.
10 - Cover with remaining bread slices, buttered side up. Cook for 2 to 3 minutes per side until golden brown and cheese is melted.
11 - Cut sandwiches in half and serve hot alongside the bisque, garnished with extra fresh basil leaves.