For a lighter version of this soup, use milk in place of the half & half. Slideshow: More Warming Soup Recipes
In a large heavy pot, heat the butter over medium high heat until hot. Stir in the onions, garlic, 3/4 teaspoon salt, and 1/2 teaspoon pepper and cook, stirring occasionally, until pale golden, about 6 minutes. Peel and dice the potatoes. Stir in the stock and potatoes then bring to a gentle boil. Cook, stirring occasionally, until the potatoes are very soft and starting to fall apart, 45 minutes to 1 hour. Stir in the half & half, then in a blender, puree the soup in batches, until smooth. Season the soup with salt and pepper to taste and serve garnished with parsley and additional half & half.