Melt butter in a large saucepan over medium-low heat. Add leeks, onions, and garlic and cook, covered, over medium-low, stirring occasionally, until very soft, 20-30 minutes. Add the potatoes and the chicken broth, raise the heat, bring to a low boil, and cook until the potatoes are very soft, 20-25 minutes.

Remove from heat and cool slightly. Working in batches, transfer to a food processor fitted with a metal blade and process until smooth; return to saucepan placed over low heat. Add the half & half and heat through; do not boil. Add salt and pepper to taste; garnish with green onions and sour cream.



Note: You can process the soup with a blender, but the food processor will yield the smoothest soup.