The secret to this simple soup is simmering the garlic, which tames its bite. The liquid for the soup is equal parts vegetable broth and water; for a stronger flavor, replace some of the water with broth. A green salad and crusty bread round out the meal.
Heat oil in large, heavy saucepan over medium heat. Add onion, and cook, stirring often, 10 minutes, or until golden. Add broth, 4 cups water, potatoes and garlic, and bring to a boil. Reduce heat to medium-low, cover and simmer 20 minutes, or until potatoes are very tender. Cool slightly.
Coarsely purée soup in blender or food processor 1 cup at a time, about 20 seconds per batch, or purée in pot with immersion blender. Do not overprocess. Return soup to pan. Season to taste with salt and pepper. Simmer until heated through. Ladle soup into bowls, and serve immediately.