01 - Heat olive oil in a large pot over medium heat. Add diced onion and cook 5 to 6 minutes until translucent. Add minced garlic and sauté 1 minute until fragrant.
02 - Incorporate 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 chopped basil. Puree bisque 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. Adjust seasoning to taste.
05 - Butter one side of each bread slice. Heat a skillet over medium heat. Place 4 slices buttered side down, layer with cheddar, and top with remaining bread slices buttered side up.
06 - Cook sandwiches 3 to 4 minutes on each side until golden brown and cheese is melted. Remove from heat and slice diagonally.
07 - Ladle hot bisque into bowls and garnish with extra basil leaves. Serve grilled cheese sandwiches on the side.