01 - Heat olive oil in a large pot over medium heat. Add diced onion and sauté until translucent, about 5 to 6 minutes. Add minced garlic and cook for an additional minute until fragrant.
02 - Combine crushed tomatoes, vegetable broth, sugar, salt, black pepper, oregano, and optional red pepper flakes in the pot. Bring to a simmer, cover, and cook gently for 20 minutes.
03 - Remove pot from heat and stir in chopped basil. Puree the soup using an immersion blender or carefully in batches with a blender until smooth.
04 - Return soup 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 with softened unsalted butter.
06 - Place four bread slices, buttered side down, on a preheated skillet over medium heat. Top each with a slice of cheddar cheese and cover with remaining bread slices, buttered side up. Cook 3 to 4 minutes per side until bread is golden brown and cheese is melted.
07 - Ladle the hot bisque into bowls and garnish with extra fresh basil. Slice the grilled cheese sandwiches diagonally and serve alongside.