Heat the olive oil in a large pot over medium heat. Add the chopped onion and cook for about 5 minutes, until softened and translucent.
Stir in the minced garlic and cook for another minute, until fragrant.
Add the diced tomatoes (with their juices), vegetable broth, sugar, dried basil, salt, and black pepper to the pot. Bring to a simmer.
Reduce the heat to low and let it cook uncovered for about 20 minutes, stirring occasionally.
Once the soup has simmered, remove the pot from heat. Using a blender or immersion blender, puree the soup until smooth.
If you prefer a creamier soup, stir in the heavy cream and heat for an additional 2-3 minutes, but do not bring to a boil.
Serve hot, garnished with fresh basil leaves if desired.