01 - Heat olive oil in a large saucepan over medium heat. Add onion and sauté until translucent, approximately 5 minutes.
02 - Add minced garlic and cook for 1 minute, stirring frequently to prevent browning.
03 - Add canned tomatoes with juices, vegetable broth, sugar, salt, and pepper. Bring to a simmer and cook uncovered for 20 minutes, stirring occasionally.
04 - Combine basil leaves, pine nuts, garlic, Parmesan, and salt in a food processor. Pulse until finely chopped. With the motor running, slowly drizzle in olive oil until a smooth paste forms. Set aside.
05 - Use an immersion blender to purée the soup until smooth, or transfer to a blender in batches and blend until velvety.
06 - Stir in the heavy cream and heat gently for 2-3 minutes. Taste and adjust seasoning as needed.
07 - Ladle soup into bowls and swirl 1-2 teaspoons of basil pesto into each serving.
08 - Serve immediately, garnished with extra basil or a drizzle of olive oil if desired.