Heat oil in a large saucepan over medium heat. Add celery and onions; cook until soft, 3-5 mins. Add garlic; cook 30 seconds, stirring constantly. Stir in the broth, salt, tomatoes, milk and sugar; bring to a boil. (When you add the milk it will curdle instantly but when you blend it later these curdles will get chopped up. Milk is totally optional too.) Reduce heat; simmer 20 minutes. Stir in basil and parsley.
Place half of the soup in a blender; process until smooth. Pour pureed soup into a bowl, and repeat procedure with remaining soup. Season with salt and pepper if needed. Garnish with basil leaves, if desired.