1. In a large pot, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
2. Add the minced garlic and cook for an additional minute.
3. Pour in the crushed tomatoes and vegetable broth. Stir in the dried basil, sugar, salt, and pepper.
4. Bring to a simmer and let cook for 15 minutes, allowing the flavors to meld.
5. Remove from heat and use an immersion blender to puree the soup until smooth. Alternatively, carefully transfer to a blender in batches.
6. Stir in the heavy cream and return to low heat to warm through.
7. Serve hot, garnished with fresh basil leaves.