01 - Melt butter in a large pot over medium heat. Add diced onion, carrot, and minced garlic; sauté for 5 minutes until softened and fragrant.
02 - Stir in tomato paste and cook 1 minute. Add diced tomatoes with juice, vegetable broth, sugar, salt, black pepper, oregano, and bay leaf. Bring mixture to a simmer.
03 - Reduce heat to low, cover, and simmer for 20 minutes, stirring occasionally.
04 - Remove bay leaf and stir in fresh basil leaves.
05 - Puree soup using an immersion blender or transfer in batches to a countertop blender until smooth.
06 - Return pureed soup to low heat. Stir in heavy cream and Parmesan cheese if using. Heat gently for 2 to 3 minutes without boiling.
07 - Taste and adjust seasoning as needed. Serve hot, garnished with additional fresh basil.