01 - Heat olive oil in a large pot over medium heat. Add diced onion and sauté for 5 to 6 minutes until translucent. Add minced garlic and cook for an additional minute until fragrant.
02 - Stir in crushed tomatoes, vegetable broth, sugar, salt, black pepper, oregano, and red pepper flakes if using. Bring mixture to a simmer, cover, and cook for 20 minutes.
03 - Remove pot from heat. Add chopped fresh basil and puree the soup until smooth using an immersion blender or standard blender in batches.
04 - Return bisque to low heat. Stir in heavy cream and gently simmer for 5 minutes. Taste and adjust seasoning as desired.
05 - Butter one side of each bread slice. Place four slices buttered side down on a skillet heated over medium heat. Layer each with cheddar cheese slices, then top with the remaining bread slices, buttered side up.
06 - Cook grilled cheese sandwiches for 3 to 4 minutes per side until bread is golden and cheese is fully melted. Remove from skillet and slice diagonally.
07 - Ladle hot bisque into bowls, garnish with extra fresh basil, and serve with grilled cheese sandwiches on the side.