In a large pot, heat olive oil over medium heat. Add the chopped onion and sauté until it becomes translucent.

Incorporate the minced garlic and cook for another minute, allowing the flavors to meld.

Stir in the crushed tomatoes, chicken or vegetable broth, sugar, dried basil, salt, and pepper. Bring this mixture to a gentle simmer.

Let it cook for about 15-20 minutes, stirring occasionally to prevent sticking.

Use an immersion blender to blend the soup until it's smooth, or carefully transfer to a blender in batches.

Return the soup to the pot and stir in the heavy cream. Heat through, but take care not to boil.

Serve hot, garnished with fresh basil if desired.