01 - Heat olive oil in a large pot over medium heat. Add chopped onion and cook until soft and translucent, about 5 minutes.
02 - Stir in minced garlic and sauté 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 mixture to a boil, then reduce heat and simmer uncovered for 20 minutes, stirring occasionally.
05 - Remove from heat and purée the soup until smooth using an immersion blender or a countertop blender in batches.
06 - Return soup to low heat. Stir in heavy cream and butter until melted and fully incorporated. Adjust seasoning to taste.
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 a slice of cheddar cheese and cover with remaining bread slices, buttered side up.
09 - Cook for 2 to 3 minutes per side until bread is golden brown and cheese has melted.
10 - Allow sandwiches to cool slightly, then cut each into strips suitable for dipping.
11 - Ladle hot soup into bowls and serve alongside grilled cheese dippers.