01 - Heat olive oil in a large saucepan over medium heat. Add chopped onion and carrot; sauté for 5 minutes until softened and fragrant.
02 - Stir in minced garlic and cook for 1 minute until aromatic, being careful not to brown.
03 - Add tomatoes with juices, vegetable broth, sugar, salt, pepper, and oregano. Bring to a boil, then reduce heat and simmer uncovered for 20 minutes to develop flavors.
04 - Remove from heat and stir in chopped fresh basil leaves, allowing them to wilt slightly.
05 - Use an immersion blender to puree until completely smooth and velvety. Alternatively, transfer to a countertop blender in batches, blending carefully with hot liquid.
06 - Return soup to low heat. Stir in heavy cream and heat gently for 2-3 minutes until warmed through. Do not boil to prevent cream from separating.
07 - Taste and adjust seasoning with additional salt and pepper if needed. Ladle into bowls and garnish with extra fresh basil leaves and a drizzle of olive oil or splash of cream.