Heat oven to 425 F. Put each potato piece cut-side down through a ricer with its smallest die, placed over a large bowl. Reserve the skins, removing and discarding any clinging potato flesh. Scatter the skins on a parchment lined half sheet pan and toss with the olive oil and 1/4 teaspoon of the salt. Place in the oven and bake for 10 minutes, or until crisp. Set aside to cool, and reserve for garnishing the soup.
Melt the butter in a 6-7 quart heavy bottom pot or Dutch oven over medium heat. Add the leeks and garlic and cook until translucent, 4-5 minutes. 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, whisking, to remove any clumps. If a smoother texture is desired, blend with an immersion blender for 30 seconds to 1 minute. Season with the salt and pepper. Remove from the heat and stir in the sherry vinegar.
Ladle into bowls and garnish with chives and crispy potato skins.