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