In a large stock pot, melt the butter over medium heat. Stir in the green garlic and leek, and cook for 3-4 minutes, stirring frequently, until beginning to soften. Stir in the potatoes, and cook for 1 minute. Pour in the broth, and just enough water to cover the vegetables. Raise heat to medium-high, and bring to a boil. Reduce heat to low, then simmer uncovered, stirring occasionally, until the potatoes are tender. Allow to cool, then refrigerate to chill completely.