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 - Incorporate the minced garlic into the pan and cook for 1 minute until fragrant.
03 - Stir in chopped tomatoes, tomato paste, vegetable broth, sugar, salt, and black pepper. Bring the mixture to a gentle simmer.
04 - Cover the pan and cook for 20 minutes, stirring occasionally to blend flavors.
05 - Use an immersion blender or transfer carefully to a blender and puree the soup until smooth.
06 - Return the pureed soup to low heat, stir in the heavy cream, and warm gently for 3 to 4 minutes. Adjust seasoning if necessary.
07 - Place basil leaves, Parmesan, pine nuts, and garlic in a food processor. Pulse until finely chopped.
08 - While processing, gradually drizzle in olive oil until the pesto achieves a smooth consistency. Season with a pinch of salt.
09 - Ladle the warm soup into bowls and swirl a spoonful of basil pesto into each serving immediately before serving.