In a large pot over medium heat, heat the olive oil. Add the chopped onion and sauté until soft and translucent, about 5-7 minutes. Add the minced garlic and cook for an additional 1 minute, stirring frequently.
Stir in the crushed tomatoes and vegetable broth. Add the sugar, dried basil, and dried oregano. Bring the mixture to a gentle boil.
Reduce the heat to low, cover the pot, and let the soup simmer for 20 minutes, allowing the flavors to meld.
Remove the pot from heat. Use an immersion blender to purée the soup until smooth. Alternatively, carefully transfer the soup to a blender in batches and blend until smooth. Be cautious with hot liquids.
Return the puréed soup to low heat. Stir in the heavy cream until fully incorporated. Season with salt and freshly ground black pepper to taste. Heat the soup gently for another 5 minutes, but do not let it boil.
Garnish with fresh basil leaves or parsley if desired. Serve hot, possibly with crusty bread or a grilled cheese sandwich.