Sauté the aromatics: Heat olive oil in a large pot over medium heat. Add chopped onion and cook for 5 minutes until softened. Stir in minced garlic and cook for 30 seconds.
Add tomatoes: Pour in the canned tomatoes with their juice. Use a spoon to gently crush them.
Simmer: Add vegetable broth, sugar, salt, and pepper. Bring to a boil, then reduce heat and simmer uncovered for 15–20 minutes to develop the flavor.
Blend until creamy: Use an immersion blender (or transfer to a stand blender) to puree the soup until smooth and velvety.
Add cream and basil: Stir in heavy cream and chopped basil. Simmer for another 2 minutes on low heat.
Serve: Pour into bowls and garnish with Parmesan cheese or extra basil. Serve warm with crusty bread or grilled cheese.
