01 - Heat olive oil in a large saucepan over medium heat. Add finely chopped onion and cook until softened and translucent, approximately 5 minutes.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Add crushed tomatoes, vegetable broth, tomato paste, sugar, salt, and black pepper. Stir to combine and bring to a simmer.
04 - Reduce heat to low, cover, and simmer gently for 20 minutes, stirring occasionally.
05 - Remove from heat, stir in chopped basil, and purée the soup until smooth using an immersion blender or countertop blender in batches.
06 - Return to low heat, stir in heavy cream, and warm gently. Adjust seasoning as needed. Keep warm until serving.
07 - Spread softened butter evenly on one side of each bread slice.
08 - Place 4 slices, buttered side down, in skillet over medium heat. Top each with 2 cheese slices, then cover with remaining bread, buttered side up.
09 - Cook sandwiches until golden brown and cheese is melted, about 3 to 4 minutes per side.
10 - Remove from skillet, allow to cool for 1 minute, then slice each sandwich into 3 to 4 strips.
11 - Ladle bisque into bowls, garnish with extra basil, and serve alongside grilled cheese soldiers for dipping.