Heat olive oil in a large pot over medium heat. Add chopped onion and sauté until translucent, about 5 minutes.

Add minced garlic and cook for another minute until fragrant, stirring constantly to prevent burning.

Pour in the crushed tomatoes and vegetable broth. Stir well to combine.

Add sugar, dried basil, dried oregano, salt, and pepper. Bring the mixture to a simmer and let it cook for 15-20 minutes, stirring occasionally.

Use an immersion blender to puree the soup until smooth. Alternatively, transfer the soup to a blender in batches and blend until smooth.

Stir in the heavy cream and heat through for another 2-3 minutes. Adjust seasoning if needed.

Ladle the soup into bowls, garnish with fresh basil leaves, and serve hot with crusty bread.