Put the potatoes, cut-side down, through a ricer with its smallest die. Set aside in a medium mixing bowl. Reserve the skins for Potato Skin Crisps.
In a large saucepot over high heat, melt the butter and add the leeks and garlic. Cook over medium heat until they are translucent. Add the hot stock and stir to combine.
In a separate bowl, whisk together the riced potatoes, buttermilk, sour cream, and grated Parmesan. Add this mixture to the soup, stirring constantly. Season with salt and pepper. Remove from the heat and add the sherry vinegar.
Ladle into bowls and garnish with chives and Potato Skin Crisps, if desired.