01 - Heat olive oil in a large pot over medium heat. Add chopped onion and sauté until soft and translucent, about 5 minutes.
02 - Stir in minced garlic and cook for 1 minute until fragrant.
03 - Add crushed tomatoes, vegetable broth, sugar, dried basil, dried oregano, salt, and black pepper. Stir to combine.
04 - Bring to a boil, then reduce heat to low and simmer uncovered for 20 minutes, stirring occasionally.
05 - Remove from heat and use an immersion blender or transfer carefully to a blender in batches to purée until smooth.
06 - Return puréed soup to low heat. Stir in heavy cream and butter until melted and the soup is creamy. Adjust seasoning as needed.
07 - Spread softened butter on one side of each bread slice.
08 - Place four slices of bread, buttered side down, on a skillet over medium heat. Top each with cheddar slice, then cover with remaining bread, buttered side up.
09 - Cook sandwiches for 2 to 3 minutes per side until bread is golden brown and cheese is melted.
10 - Allow sandwiches to cool slightly, then cut each into strips for dipping.
11 - Ladle hot soup into bowls and serve alongside grilled cheese dippers.