01 - Heat olive oil in a large pot over medium heat. Add diced onion and cook for 5 to 6 minutes until translucent. Stir in minced garlic and cook for 1 minute until fragrant.
02 - Add crushed tomatoes, vegetable broth, sugar, salt, black pepper, oregano, and crushed red pepper flakes. Bring to a simmer, cover, and cook for 20 minutes.
03 - Remove from heat and stir in fresh basil leaves. Puree the mixture until smooth using an immersion blender or regular blender in batches.
04 - Return the bisque to low heat. Stir in heavy cream and gently simmer for 5 minutes. Adjust seasoning as needed.
05 - Butter one side of each bread slice.
06 - Place four slices of bread, buttered side down, on a skillet over medium heat. Top each with cheddar cheese slices, then cover with remaining bread slices, buttered side up.
07 - Cook for 3 to 4 minutes per side until the bread is golden brown and the cheese is melted. Remove from skillet and slice diagonally.
08 - Ladle hot bisque into bowls, garnish with extra fresh basil, and serve grilled cheese sandwiches alongside.