01 - Heat olive oil in a large saucepan over medium heat. Add the chopped onion and sauté for 5 minutes until soft and translucent.
02 - Stir in the minced garlic and cook for 1 minute until fragrant.
03 - Incorporate chopped tomatoes, tomato paste, vegetable broth, sugar, salt, and black pepper. Bring mixture to a simmer.
04 - Cover and simmer the mixture for 20 minutes, stirring occasionally to meld flavors.
05 - Using an immersion blender or countertop blender, carefully puree the soup until fully smooth.
06 - Return the pureed soup to low heat. Stir in heavy cream and warm gently for 3 to 4 minutes. Adjust seasoning as needed.
07 - In a food processor, combine basil leaves, Parmesan, pine nuts, and garlic. Pulse until finely chopped.
08 - With the processor running, slowly drizzle in olive oil until pesto attains a smooth consistency. Season with a pinch of salt.
09 - Ladle the soup into bowls and finish each with a swirl of basil pesto before serving.