01 - Heat 2 tablespoons olive oil in a large saucepan over medium heat. Add chopped onion and sauté until translucent, approximately 5 minutes.
02 - Add minced garlic to the pan and cook for 1 minute while stirring frequently.
03 - Add canned tomatoes with their 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 clove, Parmesan cheese, and a pinch of salt in a food processor. Pulse until finely chopped. With the motor running, slowly drizzle in 1/4 cup olive oil until a smooth paste forms. Set aside.
05 - Use an immersion blender to purée the soup until smooth, or carefully transfer in batches to a standard blender.
06 - Stir in 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.