Heat the oil in a large stockpot over medium heat. Stir in the onions and garlic, and saute until onions are golden and tender, about 10 minutes.
Raise the heat to high, stir in all the remaining ingredients, and bring the soup to a boil. Lower the heat to a lively simmer and cook about 30 minutes, or until the potatoes are tender and the soup has thickened.
Discard the bay leaves. Remove about 2 cups of the soup and puree in a blender or food processor. Return it to the soup and stir to blend. This soup?s flavor will intensify with time, so don?t hesitate to make it a few days in advance.