01 - Heat olive oil in a large saucepan over medium heat. Add the chopped onion and cook for 5 minutes until soft and translucent.
02 - Stir in the minced garlic and cook for 1 minute until fragrant.
03 - Add chopped tomatoes, tomato paste, vegetable broth, sugar, salt, and black pepper. Bring mixture to a simmer.
04 - Cover and cook for 20 minutes, stirring occasionally to blend flavors.
05 - Use an immersion blender or transfer carefully to a blender and puree soup until smooth.
06 - Return the pureed soup to low heat. Stir in heavy cream and warm gently for 3 to 4 minutes. Adjust seasoning to taste.
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 is smooth. Season with a pinch of salt.
09 - Ladle the hot soup into bowls and swirl a spoonful of basil pesto into each before serving.